Questions on Algebra: Quadratic Equation answered by real tutors!

Tutors Answer Your Questions about Quadratic Equations (FREE)

Question 395314: I am totally confused by the factoring results my text says is the answer: The equation is
3x^2 + x - 2 = 0
They say the factor of this is
(3x - 2)(x + 1)
Why isn't it -1, +2? Isn't the product of -2 suppose to equat the sum of 1 ?
Please show me why their answer is correct? I even tried using the ac Method with no results.
Click here to see answer by ewatrrr(10682)

Question 395297: A rectangular skating rink has length 22m and width 30m. The rink is made larger by extending the width and length by the same amount such that the area of the new rink is 825 m^2. Create a quadratic equation to models this situation and use it to determine the new dimensions of the new rink.

Note: the length of one side and the width of one side, not all the way around.
Please help me.
Click here to see answer by ankor@dixie-net.com(15624)

Question 395305: solve and find the value for x which satisfies the equation
2x^2-4=7x

Click here to see answer by jim_thompson5910(28476)

Question 395382: 1. 5/2x^2-3/2x-1/4=0
2. 12m^2-192=0
if you could write out how to do it it would help me so much thanks
Click here to see answer by jim_thompson5910(28476)

Question 395421: If the numerical value of the area of a rectangle is 19 more than 2 times the perimeter, and the length is 2 more than the width, what is the width?
Area = L * W
2x + 19
w = X
l = X + 2
X(X + 2) = 2x + 19 ?
x^2 + 2x = 2x + 19 + x + 2

Click here to see answer by jrfrunner(365)

Question 395429: When the area of a rectangle is 3 times the length and the lenght is 1 more than twice the width, what are the demensions?
I know somthing is missing in my formula. Please help? Thanks.
A = L*W
W = x
L = 2x + 1
x(2x + 1) = 3(2x + 1)
2x^2 + x = 6x + 3
2x^2 + 5x + 3
(2x + 3)(x+1)

Click here to see answer by stanbon(57219)

Question 395357: write a quadratic equation having the given numbers as solutions
-5 and -3
Click here to see answer by MathLover1(6614)

Question 395439: Give exact and approximate solutions to three decimal places.
X^2+12X+36=64
Click here to see answer by jim_thompson5910(28476)

Question 395293: The sum of two numbers is 10 and the sum of their squares is a minimum. Algebraically determine the function that models the sum of their squares and use it to find the two numbers.
Click here to see answer by robertb(4012)

Question 395288: An Olympic ski jumper skis off a spring board. Her height h, in meters, above the ground, t seconds after she jumps, is given by h(t)= -4.9t^2 + 20t +15. Algebraically determine the approximate instantaneous rate of change in her height at 2 seconds and describe what is happening at that time.
Click here to see answer by ankor@dixie-net.com(15624)

Question 395569: find the vertex, the line of symmetry, and the maximim or minimum value of the quadratic function, and graph the function on paper.
f(x) = 2x^2+2x+4
what is the x-coordinate of the vertex? (type a simplified fraction)
Click here to see answer by lwsshak3(6460)

Question 395613: Find the vertex and x-intercept(s) for the quadratic function.
f(x)= -3x^2+2x+3
Round to the nearest hundredth if necessary.
If there is more than one x-intercept, separate them with commas.
Click here to see answer by ewatrrr(10682)

Question 395575: find the x-intercepts and y-intercepts
f(x) = -x^2 +2x+15
The x-coordinates of the intercepts are x= ___
Click here to see answer by ewatrrr(10682)

Question 395567: find the vertex, the line of symmetry, and the maximim or minimum value of the quadratic function, and graph the function on paper.
f(x) = 3x^2-18x+14
what is the vertex (type an ordered pair)
Click here to see answer by ewatrrr(10682)

Question 395560: find the vertex, the line of symmetry, and the maximim or minimum value pf f(x). Graph the function.
f(x)= -(x+9)^2-4
the vertex is (type an ordered pair)
Click here to see answer by ewatrrr(10682)

Question 395555: find the vertex, the line of symmetry, and the maximum or minimum value of f(x). Graph the function.
f(x)= -5(5+3)^2 + 8
the vertex is (type an ordered pair)
Click here to see answer by ewatrrr(10682)

Question 395566: find the vertex, the line of symmetry, and the maximim or minimum value of the quadratic function, and graph the function on paper.
f(x) = x^2 -10x-4
what is the vertex (type an ordered pair)
Click here to see answer by ewatrrr(10682)

Question 395572: Aki's bicycle designs has determined that when x hundred bicycles are built, the average cost per bicycle is given by C(x) = 0.1x^2 - 1.6x + 8.78, where C(x) is in hundreds of dollars. How many bicycles should the shop build to minimize the average cost per bucycle?
The shop should build ___ bicycles?
Click here to see answer by jrfrunner(365)

Question 395630: To calculate the quadratic equation given 3 sides A,B,C your program should be interactive [hint-x=[-b+vb2-4ac]/2a
Click here to see answer by richard1234(5390)

Question 395652: Please walk me thru this problem, especially the process for determining each of the factors:
Solve: 5x^2 - 8x +3 = 0. My text says that the factors are (5x-3)(x-1). I don't understand how they got this. thank you.
Click here to see answer by ewatrrr(10682)

Question 395655: Please walk me thru this problem, especially how they got their factors:
Solve: 3x^2 + x - 2 = 0. They say that the factors are(3X-2)(X+1). Thank you..
Click here to see answer by ewatrrr(10682)

Question 395690: Hello. I am stumped on a homework assignment. I have to solve a quadratic equation using two methods. I have solved the equation using factoring and now have to figure out how to solve it by completing the square method. The equation I have is z^2+z-2=0. Any help would be greatly appreciated.
Thank you.
Click here to see answer by Alan3354(30959)

Question 395574: A carpenter is building a rectangular room with a fixed perimeter of 304 ft. What dimensions would yield the maximum area? What is the maximum area?
The length that would yield the maximum area is ___ ft.
Click here to see answer by solver91311(16868)

Question 395731: Help please. I have an assignment to find a real world situation where quadratic equations are used. I don't have trouble finding them, just the ones I do find I have no idea how to explain. I really appreciate any help!
Explore and find a real-world application of a quadratic equation, whether it is from the realm of physics, finance, or anything else. Write a paragraph about what you find. In your description,
* show the equation.
* explain what the variable represents in real terms.
* describe what the equation models in real terms.
Click here to see answer by richard1234(5390)

Question 395766: Hello. I am really stuck on my homework and need help. I am trying to solve this quadratic equation by factoring. Can anyone help? Thank you!
x^2+4x=12
Click here to see answer by ewatrrr(10682)

Question 395993: A high school is planning to build a new field surrounded by a running track. The perimeter of the track is 500m.A rectangle field inside track with maximum area, what are the dimensions ?
Click here to see answer by Alan3354(30959)

Question 396016: solve each equation using the quadratic formula:
1.) 4x^2+x-5=0
2.) 2x^2-5x+2=0
3.)3x^2+7=-6x
4.) 7x^2-x-12=0
Click here to see answer by mananth(12270)

Question 396120: How would you solve this?
m4 +13m2 − 48 = 0
would you separate the equation out so it's
m2(m2+13)-48=0?
Click here to see answer by Alan3354(30959)

Question 396264: Completing the square.
Please walk me through each step. the text says the answers are x=10, x=-2
x^2 - 8x - 20 = 0
thank you
Click here to see answer by ewatrrr(10682)

Question 396277: a store is having a sale and every thing is 1/4 off the regular price write and eqations to express the cost of 29$ jeans
Click here to see answer by ewatrrr(10682)

Question 396624: There are two positive numbers such that one is 6 less than twice the other.The difference of the squares of the two numbers is 1311.Find the numbers.
Click here to see answer by ewatrrr(10682)

Question 396661: Trying to explain how to split the middle term when solving quadratic equations to my 16 yr old now taking algebra.
Example: 7a^2 + 53a + 28
My instinct is to factor it out to:
(7a + 49a +4) + (1a + 4a + 7)
but this is not working when you multiply it out... I just can't quite remember how to split the middle term
Thanks
Click here to see answer by CharlesG2(828)

Question 396995: how do you write a quadratic function in standard form whose graph passes through the given points: (2,7) (3,2) and (5,4)?
Click here to see answer by stanbon(57219)

Question 397042: x^2-4x-5=0
Click here to see answer by jim_thompson5910(28476)

Question 397039: Find two numbers whose sum is 54 such that the sum of their squares is a minimum. (If a solution has a multiplicity of two, enter it in consecutive answer boxes.)
smaller number=
larger number=
Click here to see answer by richard1234(5390)

Question 396941: Find the largest integral value of k such that the roots of 2x^2-5x+k are real.
Click here to see answer by richard1234(5390)

Question 397233: Demonstrate how your quadratic equation is solved by the Quadratic Formula. Explain your steps.
7. $x^2 + 13= 4x$

Click here to see answer by MathLover1(6614)

Question 397228: the quadratic equation exercises that are attached to this note and demonstrate how your quadratic equation is solved by the Factoring Method. Explain your steps. Demonstrate how your quadratic equation expression is solved by the Square Root Property. Explain your steps. Two quadratic equations (similar to the ones you chose to explain above) for your classmates to solve using the algorithms to work with quadratic equations.
12. $(x – 9)^2= 34$
16. $(t – 2)^2= 25$

Click here to see answer by MathLover1(6614)

Question 397270: Write a quadratic equation in the variable x having the given numbers as solutions. Type the equation in standard form,
Solution: 4, only solution
The equation is ____=0
Click here to see answer by MathLover1(6614)

Question 397275: Use the quadratic formula to solve the equation.

The solution set is{____}.
Click here to see answer by ewatrrr(10682)

Question 397241: This is a quadratic function question but I didn't see that as an option to select.
A ball is tossed straight up from the top of a 1,127 foot tall building with an initial speed of 44 feet per second. The height h(t) of the ball t seconds after it is thrown is given by h(t)= -16t^2 + at + b (t^2 is my way of saying t-squared), where a is the initial speed of the ball and b is the initial height from which it is thrown.
A. How long was the ball in the air before it hit the street below? The answer is 9.88 seconds but I can't figure out how to get to the answer. I set it up as follows:
h(t)= -16t^2 + 44t + 1127
B. What is the maximum height the ball reaches? Answer is 1157.25 feet- again not sure how to get this.
C. How long does it take the ball to reach its maximum height? Answer is 1.37 seconds.
Even if you can just help with letter A. that would be a huge help.
Thank You
Click here to see answer by stanbon(57219)

Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485, 1486..1530, 1531..1575, 1576..1620, 1621..1665, 1666..1710, 1711..1755, 1756..1800, 1801..1845, 1846..1890, 1891..1935, 1936..1980, 1981..2025, 2026..2070, 2071..2115, 2116..2160, 2161..2205, 2206..2250, 2251..2295, 2296..2340, 2341..2385, 2386..2430, 2431..2475, 2476..2520, 2521..2565, 2566..2610, 2611..2655, 2656..2700, 2701..2745, 2746..2790, 2791..2835, 2836..2880, 2881..2925, 2926..2970, 2971..3015, 3016..3060, 3061..3105, 3106..3150, 3151..3195, 3196..3240, 3241..3285, 3286..3330, 3331..3375, 3376..3420, 3421..3465, 3466..3510, 3511..3555, 3556..3600, 3601..3645, 3646..3690, 3691..3735, 3736..3780, 3781..3825, 3826..3870, 3871..3915, 3916..3960, 3961..4005, 4006..4050, 4051..4095, 4096..4140, 4141..4185, 4186..4230, 4231..4275, 4276..4320, 4321..4365, 4366..4410, 4411..4455, 4456..4500, 4501..4545, 4546..4590, 4591..4635, 4636..4680, 4681..4725, 4726..4770, 4771..4815, 4816..4860, 4861..4905, 4906..4950, 4951..4995, 4996..5040, 5041..5085, 5086..5130, 5131..5175, 5176..5220, 5221..5265, 5266..5310, 5311..5355, 5356..5400, 5401..5445, 5446..5490, 5491..5535, 5536..5580, 5581..5625, 5626..5670, 5671..5715, 5716..5760, 5761..5805, 5806..5850, 5851..5895, 5896..5940, 5941..5985, 5986..6030, 6031..6075, 6076..6120, 6121..6165, 6166..6210, 6211..6255, 6256..6300, 6301..6345, 6346..6390, 6391..6435, 6436..6480, 6481..6525, 6526..6570, 6571..6615, 6616..6660, 6661..6705, 6706..6750, 6751..6795, 6796..6840, 6841..6885, 6886..6930, 6931..6975, 6976..7020, 7021..7065, 7066..7110, 7111..7155, 7156..7200, 7201..7245, 7246..7290, 7291..7335, 7336..7380, 7381..7425, 7426..7470, 7471..7515, 7516..7560, 7561..7605, 7606..7650, 7651..7695, 7696..7740, 7741..7785, 7786..7830, 7831..7875, 7876..7920, 7921..7965, 7966..8010, 8011..8055, 8056..8100, 8101..8145, 8146..8190, 8191..8235, 8236..8280, 8281..8325, 8326..8370, 8371..8415, 8416..8460, 8461..8505, 8506..8550, 8551..8595, 8596..8640, 8641..8685, 8686..8730, 8731..8775, 8776..8820, 8821..8865, 8866..8910, 8911..8955, 8956..9000, 9001..9045, 9046..9090, 9091..9135, 9136..9180, 9181..9225, 9226..9270, 9271..9315, 9316..9360, 9361..9405, 9406..9450, 9451..9495, 9496..9540, 9541..9585, 9586..9630, 9631..9675, 9676..9720, 9721..9765, 9766..9810, 9811..9855, 9856..9900, 9901..9945, 9946..9990, 9991..10035, 10036..10080, 10081..10125, 10126..10170, 10171..10215, 10216..10260, 10261..10305, 10306..10350, 10351..10395, 10396..10440, 10441..10485, 10486..10530, 10531..10575, 10576..10620, 10621..10665, 10666..10710, 10711..10755, 10756..10800, 10801..10845, 10846..10890, 10891..10935, 10936..10980, 10981..11025, 11026..11070, 11071..11115, 11116..11160, 11161..11205, 11206..11250, 11251..11295, 11296..11340, 11341..11385, 11386..11430, 11431..11475, 11476..11520, 11521..11565, 11566..11610, 11611..11655, 11656..11700, 11701..11745, 11746..11790, 11791..11835, 11836..11880, 11881..11925, 11926..11970, 11971..12015, 12016..12060, 12061..12105, 12106..12150, 12151..12195, 12196..12240, 12241..12285, 12286..12330, 12331..12375, 12376..12420, 12421..12465, 12466..12510, 12511..12555, 12556..12600, 12601..12645, 12646..12690, 12691..12735, 12736..12780, 12781..12825, 12826..12870, 12871..12915, 12916..12960, 12961..13005, 13006..13050, 13051..13095, 13096..13140, 13141..13185, 13186..13230, 13231..13275, 13276..13320, 13321..13365, 13366..13410, 13411..13455, 13456..13500, 13501..13545, 13546..13590, 13591..13635, 13636..13680, 13681..13725, 13726..13770, 13771..13815, 13816..13860, 13861..13905, 13906..13950, 13951..13995, 13996..14040, 14041..14085, 14086..14130, 14131..14175, 14176..14220, 14221..14265, 14266..14310, 14311..14355, 14356..14400, 14401..14445, 14446..14490, 14491..14535, 14536..14580, 14581..14625, 14626..14670, 14671..14715, 14716..14760, 14761..14805, 14806..14850, 14851..14895, 14896..14940, 14941..14985, 14986..15030, 15031..15075, 15076..15120, 15121..15165, 15166..15210, 15211..15255, 15256..15300, 15301..15345, 15346..15390, 15391..15435, 15436..15480, 15481..15525, 15526..15570, 15571..15615, 15616..15660, 15661..15705, 15706..15750, 15751..15795, 15796..15840, 15841..15885, 15886..15930, 15931..15975, 15976..16020, 16021..16065, 16066..16110, 16111..16155, 16156..16200, 16201..16245, 16246..16290, 16291..16335, 16336..16380, 16381..16425, 16426..16470, 16471..16515, 16516..16560, 16561..16605, 16606..16650, 16651..16695, 16696..16740, 16741..16785, 16786..16830, 16831..16875, 16876..16920, 16921..16965, 16966..17010, 17011..17055, 17056..17100, 17101..17145, 17146..17190, 17191..17235, 17236..17280, 17281..17325, 17326..17370, 17371..17415, 17416..17460, 17461..17505, 17506..17550, 17551..17595, 17596..17640, 17641..17685, 17686..17730, 17731..17775, 17776..17820, 17821..17865, 17866..17910, 17911..17955, 17956..18000, 18001..18045, 18046..18090, 18091..18135, 18136..18180, 18181..18225, 18226..18270, 18271..18315, 18316..18360, 18361..18405, 18406..18450, 18451..18495, 18496..18540, 18541..18585, 18586..18630, 18631..18675, 18676..18720, 18721..18765, 18766..18810, 18811..18855, 18856..18900, 18901..18945, 18946..18990, 18991..19035, 19036..19080, 19081..19125, 19126..19170, 19171..19215, 19216..19260, 19261..19305, 19306..19350, 19351..19395, 19396..19440, 19441..19485, 19486..19530, 19531..19575, 19576..19620, 19621..19665, 19666..19710, 19711..19755, 19756..19800, 19801..19845, 19846..19890, 19891..19935, 19936..19980, 19981..20025, 20026..20070, 20071..20115, 20116..20160, 20161..20205, 20206..20250