Questions on Algebra: Quadratic Equation answered by real tutors!

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Question 141840: Hi I need help in understanding one of the steps in "completing the square" for a quadratic equation.Here is my problem
x^2+9x+8=0
IN the 2ND step my homework tells me that I have to multiply the equation by A, whatever value it has.Now everytime they show a model there is a different value for "A" everytime.How do I find the value of "A" for my own homework equations.Here is one of my models from my school...

Solve x^2 + 7x + 12 = 0 by completing the square.
1. Write the quadratic equation in general for and identify A and B.
A is 1 and B is 7.
2. Multiply the terms of the equation by 4A.

4A is 4: 4[x^2 + 7x + 12]= 4[0]
4x^2 + 28x + 48 = 0
3.Isolate the constant term on the right side of the equation.
4x^2 + 28x = -48
4.Add B^2 to each side of the equation.
B^2 is 49: [4x^2 + 28x] +49 = [-48]+49
4x^2 + 28x + 49 = 1
5.Factor the left side of the equation to the square of a binomial.
(2x + 7)(2x + 7) = 1
(2x + 7)^2 = 1
Now solve:
1^2 is 1, so (-1)^2 is 1, so
2x + 7 = 1 2x + 7 = -1
2x = -6 2x = -8
x = -3 x = -4

The solution set is {-4, -3}.
What I dont understand is step 2 how did they decide to multiply the equation by 4? Why dont they use any other number like 2 or 6?

I hope I gave you enough information.Thanks for your help...
Click here to see answer by solver91311(17077)

Question 141709: The length of a rectsngle is fixed at 14cm. What widths will make the perimeter greater than 86cm? the width must be bigger than ___?
Will someone help me with this I cannot do word problems at all!!!
Click here to see answer by ankor@dixie-net.com(15746)

Question 141874: Solve the following system of equations.
x+2y=7 (1)
x=8-2y (2)
How do I do this one???
Click here to see answer by rapaljer(4667)

Question 141873: Translate to an algebraic expression.
The product of 16% and some number.
I do not understand this one at all will someone help please.?
Click here to see answer by rapaljer(4667)

Question 141872: Graph the equation using the slope and y-intercept.
y = 9/4x + 7 (the 9/4 is a fraction)
HELP PLEASE
Click here to see answer by rapaljer(4667)

Question 141870: Solve. Then Graph.
7x >_ 63 (The _ is supposed to be under the >)
Would the solution be {xlx<9} ?? AND
the graph be a hollow circle on the 9 and and arrow towards the numbers higher than 9? Am I even close?

Click here to see answer by rapaljer(4667)

Question 141902: How do you find the term that should be added to the expression to make a perfect square trinomial?
x^2 + 11x
x^2 + 4/5x
how?
Click here to see answer by Earlsdon(6294)

Question 142110: SOLVE.
5/8x + 1/16x = 3/16 + x
(these are all fractions)
HELP, how do I do this? Do i have to change the 5/8 to 10/16x?
Click here to see answer by stanbon(57969)

Question 142112: Graph the inequality.
4x + 5y <_ 20 (of course the _ goes under the <)
Can someone please help me with this one?
Click here to see answer by stanbon(57969)

Question 142111: please help me graph x^2+3x=18
Click here to see answer by nabla(475)

Question 142115: How do I determine the slope of a line while looking at a line on a graph?? It says m = ??
Just take the 2 points from y and x and put it parenthsis?? y comes first correct? Am I even close?
Click here to see answer by stanbon(57969)

Question 142118: 0.4x + 3 <_ 1.2x-6
Will someone please help me.
Click here to see answer by Earlsdon(6294)

Question 142116: Soybean meal is 16% protein; cornmeal is 8% protein. How many pounds of each should be mixed together in order to get 320-lb. mixture with 15% protein?
How many pounds of the cornmeal should be in the cornmeal mixture?
How many pounds of the soybean meal should be in the mixture?
HELP I hate word problems!!!! PLEASE!
Click here to see answer by scott8148(6628)

Question 142117: Graph the eqquation and identify the y-intercept.
y + x = -8
HELP PLEASE!!!!!!
Click here to see answer by josmiceli(9817)

Question 142348: In the equation : x^a - x^b = z , where 'x' & 'z' is a positive integer, where a>b and 'a' & 'b' are positive integers. Can we find the value of 'a' & 'b' ? when the value of 'z' and 'x' is given. Is there any method. For example given eqn 2^a - 2^b = 32512. Here can we find that a=15 and b=8.
For example given eqn 3^a - 3^b = 6318. Here can we find that a=8 and b=5.
I need method to find a and b. This is the question of finding two variables in an equation. Please help me to know this. If possible please find URL where solution is present.(FROM SHIVA)
Click here to see answer by scott8148(6628)

Question 142368: A man walks at a pace of 3 miles per hour. After 2 hours he stops for a rest. Let t be time AFTER the rest. Let d be the TOTAL distance traveled since he started. Write an equation linking d and t.
Click here to see answer by scott8148(6628)

Question 142421: i need help with factoring questions such as
Click here to see answer by luckycarebear4(1)

Question 142445: what is the answer to -2x2 + 5x = 0
15c2 - 12c = 48

m2=4m - 4
Click here to see answer by checkley77(12569)

Question 142372: A high school class wants to raise money by recycling newspapers. The class decided to rent a truck at a cost of $150 for the week. The market price for recycled newspapers is $15 per ton. Write an equation representing the amount of money the class will make based on the number of tons of newspapers collected...
15*x-150= T
Click here to see answer by jojo14344(1512)

Question 142537: I need help!!! My problem is I must solve this equation by completing the square!!! The equation is r2-2r-35=0!!! Can you please help me!!!
Click here to see answer by jim_thompson5910(28717)

Question 142588: i am trying to solve the following quadratic equation, however i am unsure of how exactly to rearrange the equation in order to solve it correctly.?????
x^2 - 6x = 10 + 4x
can you help????
Click here to see answer by vleith(2825)

Question 142648: The equation y= -1777x + 27,153 can be used to predict the number y of gun deaths in the United States x years after 2000, that is x=0 corresponds to 2000, x=3 corresponds to 2003, x=4 is 2004 and so on. Predict the number of gun deaths in the year 2004 and 2007 and predict in what year the number of gun deaths will be 11,160Predicted gun deaths in 2000 and 2004 would be?? And what year will there be 11160 gun deaths?
How do I figure this out???? I was doing so good now am stuck again.
Will someone please help with this word problem??
Click here to see answer by checkley77(12569)

Question 142656: Use the intercepts to graph the equation.
x + 3y = 6
HELP PLEASE!!

Click here to see answer by checkley77(12569)

Question 142657: 8x= -56
Solve using the multiplication principle.
Would the answer be -7? Or am I way off again??
Click here to see answer by checkley77(12569)

Question 142663: -7x > 1/15
Solve using the multiplication principle. Will someone please help with this, this is my last one that I really do NOT understand. I am going to try to figure out some of the others with things I have learned from all of you here. Thanks again for your help everyone!!
Click here to see answer by vleith(2825)

Question 142661: Find the slope if it exsists. m=? Help me with this? The slope is -5?
x = -5
Click here to see answer by vleith(2825)

Question 142700: solve -m squared= -81
(i couldnt figure out how to make the square symbol)

Click here to see answer by stanbon(57969)

Question 142709: Find the vertex of the graph of the quadratic function.
f (x)=-x^2-10x-7
I'm not sure what to do here. Could you please tell me where to start and what I'm doing? Thanks
Click here to see answer by oscargut(900)

Question 142653: Solve by the substitution method.Type an ordered pair,the solution of the system is???
4x + 3y = -14
x = 5 - 5y
Help please.
Click here to see answer by oscargut(900)

Question 142652: -23 <_ 4x -6 <_ -5
The solution is {xl?<_x<_?}
Will someone show me how to do this correctly? PLEASE??
Click here to see answer by oscargut(900)

Question 142718: Im having some trouble with this one. I know how to put the problem in the right order but the y/2 has me confused. So I would appreciate help solving this one. Here it is: y^2+y/2=-3/2 The only thing I was sure about was putting it into the correct form: y^2+y/2+3/2
Click here to see answer by Edwin McCravy(8999)

Question 142711: find the vertex of the graph of the quadratic function.
x/(x-2) - 4/(x^2-4x+4)
I'm just not sure what I'm supposed to be doing or where to start.
Click here to see answer by edjones(7569)

Question 142754: Solve by
the quadratic formula
4 + 4x = 2x to 2nd power
Click here to see answer by checkley77(12569)

Question 142744: this is a word problem. The width of a rectangular gate is 2 meters (m) larger than its height. The diagonal brace measures sqrt6m. find the width and height.
I'm not sure how to set this up to solve it. Can you help? Thanks, Anne
Click here to see answer by jojo14344(1512)

Question 142742: this problem states to find b^2-4ac and the number of real solutions to each equation.
4m^2+25=20m this is what I did 4m^2+25-20m=0
a=4 b=-20 c=25
(-20)^2 -4(4)(25) = 400-400= 0
Is there any other solution to this equation and if there is what do I do to find it? Thank you for your help. Anne
Click here to see answer by scott8148(6628)

Question 142778: Thank you in advance for your help. It is appreciated. My word problem is: One leg of a right triangle is 4 inches longer than the other leg. If the length of the hypotenuse is 20 inches find the length of each leg.
Click here to see answer by jojo14344(1512)

Question 142906: this problem isn't from a book. It simply says "solve"
a^4-5a^2+4=0 Can you help me with this? Thank you, Anne
Click here to see answer by vleith(2825)

Question 142779: Thank you in advance for your help with this problem. A piece of wire 60 inches long is cut into tow pieces and then each piece is bent into the shape of square. If the sum of the areas of the two squares is 117 square inches find the length of each piece of wire.
Click here to see answer by checkley77(12569)

Question 142922: 8d fewer than 6 out of the next 20 business days. If this actually happened, might it shake you confidence in the statement p = 0.60? Might it make you suspect that p is less than 0.60? Explain.
8e more than 17 of the next 20 business days. If this actually happened, might you suspect that p is greater than 0.60? Explain.

This problem has me so stumped if you could help I would be very greatful
Click here to see answer by stanbon(57969)

Question 142943: I have tried this for hours and I need help
(6x^4-2)(x^5-7) I am sop confused on the foil method please help
Diane
Click here to see answer by jim_thompson5910(28717)

Question 142921: HELP
a)solve 4x^2=12 I have to find x for this one
b)Find the intercepts of f(x)=4x^2-12
I am totally lost on this
Thanks
Click here to see answer by Earlsdon(6294)

Question 142961: The process of writing a quadatic equation in the form (x + a)2nd power = b is called
Click here to see answer by stanbon(57969)

Question 142945: I can not figure out how to write a quadriatic equation where the answer is 3 ax^2+bx+c=0 is the formula
Thanks
Diane
Click here to see answer by Earlsdon(6294)

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