Questions on Algebra: Quadratic Equation answered by real tutors!

Tutors Answer Your Questions about Quadratic Equations (FREE)

Question 4874: The manager of a bicycle shop has found that the revenue (in dollars) from the
sale of x bicycles is given by the following equation:
R=x^2-200x
how many bicycles must be sold to produce the revenue of $12,500.
Show each step of math, and write explanation describing steps followed to arrive
at answer and these steps were chosen.
Click here to see answer by ichudov(499)

Question 4892: what is the name of the solution of the quadratic equation x squared- x-1=0?
Click here to see answer by longjonsilver(2297)

Question 4893: I have been asked to draw a position tme graph based on the following data which details a fairground ride in the first 8 seconds - but my mind has gone completely blank.
1 y = 4t^2 for first 2 seconds
2 y = -4t^2 + 32t - 32 from 2 - 6 seconds
3 y = 4t^2 - 64t + 256 from 6 - 8 seconds
Any help appreciated.

Click here to see answer by Abbey(339)

Question 4602: multiply:
5x+5/x-2*2x^2-8x+8/x^2-1
Click here to see answer by Abbey(339)

Question 4910: 5(y+2)= 17
Click here to see answer by Abbey(339)

Question 4956: Find the quotient.
3/16 divide 5/2
Click here to see answer by Abbey(339)

Question 4959: How would I translate into an algebraic expression?
The product of x + y and x - y.
Click here to see answer by Hungryfrog(2)

Question 4958: HOw can I convert to decimal and percentage?
5/8
Click here to see answer by Abbey(339)

Question 4960: How would I use the distrbutive property to factor?
7a - 35
Click here to see answer by Abbey(339)

Question 4961: How would I solve by first eliminating the fractions?
x/2 - x/3 = 5
Click here to see answer by Abbey(339)

Question 4962: How would I solve the compound inequality and write the solution set in interval notation?
-1 < 3 - 2x < 11
Click here to see answer by Abbey(339)

Question 4242: If a < b, then -a > -b. Why?
Click here to see answer by xcentaur(357)

Question 4242: If a < b, then -a > -b. Why?
Click here to see answer by ichudov(499)

Question 5008: What is the square route of 121???
Click here to see answer by longjonsilver(2297)

Question 4917: Is there a value for C (C is not = to 0) such that the trinomial
X squared + X + C is factorable?
Explain why or why not
Click here to see answer by longjonsilver(2297)

Question 5011: How do I establish the identity of the following? show steps please
1. sin theta(cot theta + tan theta) = sec theta
2. (sin theta + cos theta)^2 + (sin theta - cos theta)^2 = 2
Thanks

Click here to see answer by longjonsilver(2297)

Question 5010: I want to find all solutions of this equation.
2 sin x + square root of 3 = 0
I want the steps to solve over the inteval [0,2pi)
1. sin theta = square root of 3 over 2
2. sin 3x = neg. 1/2
3. tan ^2x + 2 tan x+1 = 0
4. cos 2x + cos x = 0
Thanks for your help so I can understand how to do these!
Click here to see answer by longjonsilver(2297)

Question 5014: I am having a problem fitting my factors into the quadratic equation. The question is as follows:
A retailer spent $48 to purchase a number of special mugs. Two of them were broken in the store, but by selling each of the remaning mugs for $3 above original cost per mug, she made a total profit of $22.00.
How many mugs were originally purchased?
**If anyone could just give my brain a push, I would be more than grateful!! It's been 15 years since I have used the quadratic equation and I am just stuck!!
Thank you in advance!!
Click here to see answer by longjonsilver(2297)

Question 5053: Q. Prove the following identity: 1 divided by 1+cosx = 1/sin^2x - 1/sinxtanx
I am at the dead end but these are my steps:
R.S.
1 divided by(sinx)(sinx)-1 divided by (sinx)(sinx/cosx)=
sin^2x+cos^2x divided by sin^2x - sin^2x+cos^2xdivided by (sin^2x/cosx)=
(sinx)(sinx)+(cosx)(cos)divided by (sinx)(sinx) - (sinx)(sinx) + (cosx)(cosx)(cosx)divided by (sinx)(sinx)=
sin^2x + cos^2x - sin^2x + cos^2x(cosx) divided by (sinx)(sinx)=
and here either
1 - cosx divided by sin^2x
or
2cos^2x(cosx)divided by sin^2x
--------
thanks mmm

Click here to see answer by longjonsilver(2297)

Question 5027: how do I find all solutions for this equation.
2 sin x + square root of 3 = 0
Thank you so much in helping me to get ahead before going back to school in the fall.
sta
Click here to see answer by rapaljer(4667)

Question 4468: can someone give me an real-world application involving either quadratic, rational, or radical equations.
Click here to see answer by rapaljer(4667)

Question 4283: What role of operations that applies when you are solving an equation has a major exception when you are solving an inequality? Why?
Click here to see answer by rapaljer(4667)

Question 5071: Q. If one complex zero of a quadratic equation is 2 + i, what is the quadratic equation in ax^2 + bx + c = 0
thanks, Mike
Click here to see answer by Earlsdon(6287)

Question 5071: Q. If one complex zero of a quadratic equation is 2 + i, what is the quadratic equation in ax^2 + bx + c = 0
thanks, Mike
Click here to see answer by ichudov(499)

Question 5070: I came across this problem trying to resolve it. I used graphing approach calculating vertices, quadratic and just seem unable to get "reasonable" or real solution.
Q. If the bus ticket is 1.60 the average number of riders is 2000. The bus company considers raising the ticket, but on every 0.10 increase they loose 100 riders. What should the bus company charge to maximize their profits.
So far I have:
(2000-100x)(1.60+0.10x)=0
y=-10x^2+40x+3200
Thanks a bunch, Mike
Click here to see answer by longjonsilver(2297)

Question 5088: Can you show me how to use the quadratic formula to solve the following equation.
x^2+16x+25=0
Thank you
Click here to see answer by rapaljer(4667)

Question 5096: (8x+5/2)(8x-5/2)
Click here to see answer by lotanez(23)

Question 5098: How do I divide this equation using a+bi form 6/2+4i
Click here to see answer by rapaljer(4667)

Question 5134: Please explain and solve the polynomial:
n to the second power/4 - 9/16
Click here to see answer by rapaljer(4667)

Question 5138: what is the factors of 2x*x-27x+36=0
Click here to see answer by rapaljer(4667)

Question 5148: how do u solve xsquared-3x=0? thank you
Click here to see answer by guapa(62)

Question 5195: please help me solve this equation using the quadratic formula

2x*1=2
2=2
Click here to see answer by ichudov(499)

Question 5115: Factor the polynomial. Please explain and solve:
32n (n is to the second power) - 80n +50
Click here to see answer by ichudov(499)

Question 5212: find two numbers such that their sum is 4 and their product is 1.
the answer is 2-radical 3 and 2+ radical 3
what is the equation?

Click here to see answer by khwang(438)

Question 5211: I've been working on word problems, but this one has me stumped.
A car travels 120 miles. A second car; traveling 10 mph faster than the first car, makes the same trip in one hour less time. Find the speed of each car.
Click here to see answer by xcentaur(357)

Question 5292: Please explain and factor the polynomial:
n^2/4 - 9/16
Click here to see answer by ichudov(499)

Question 5316: how do u do quadratic formulas?
Click here to see answer by longjonsilver(2297)

Question 5291: x^2+2x+3=0
Click here to see answer by ichudov(499)

Question 5322: if x=3 and x=-5, then form a quadratic equation. How can I do this to come out right? Thanks
Click here to see answer by arunpaul(104)

Question 5324: could someone help me factor this. I'm horrible with factoring!
x^2-12x+27
( x )( x )
-12x 1,12 2,6 3,4
27 1,27 3,9

Click here to see answer by arunpaul(104)

Question 5328: Okay... here's one that I think I solved correctly, but am not sure.... just looking for a little guidance...
Here we go!
Convert the following into the quadratic equation ax^2+bx+c=0.

I came up with 4x^2 + 3x - 10 = 0.
I did this by multiplying the a & b variables by X/X.... am I on the right track??
Thanks!
JRM
Click here to see answer by ichudov(499)

Question 5341: How do I factor this polynomial? If it can't be factored please write "prime".
Click here to see answer by rapaljer(4667)

Question 5357: I am having trouble understanding how to use the Perfect Square Trinomial Formula. my problem is:
9(x-3)^2-24(x-3)+16
I really don't even know where to begin. I have the formula:
a^2+2ab+b^2=(a+b)^2
a^2-2ab+b^2=(a-b)^2
Where do I go from here?
Click here to see answer by longjonsilver(2297)

Question 5290: 6x^2-25=0
Click here to see answer by Abbey(339)

Question 5526: Which of the following are the factors of 4b^2-16?
Click here to see answer by Abbey(339)

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