Solving for x by factoring?

Question

specifically, in these two problems:

x^2 - 2x = 11x

12x^2 - 15 = -11x

Answer 1

1. x^2 - 2x = 11x

Subtract 11x from both sides

x^2 - 2x - 11x = 0

Combine the x terms

x^2 - 13x = 0

Factor

x(x - 13) = 0

x = 0, x = 13

2. 12x^2 - 15 = -11x

Add 11x to both sides

12x^2 + 11x - 15 = 0

Factor

(3x + 5)(4x - 3) = 0

3x + 5 = 0 or 4x - 3 = 0

3x = -5 or 4x = 3

x = -5/3 or 3/4

Hope this helps you!  Please email anytime for further questions.

Answer 2

For the first one, add 2x to both sides:

x^2 = 13x

Divide both sides by x:

x = 13

The second one is kinda guess and check. Find the factors of 12 and set it up like this: (you will be using only one form of this, you just have to figure out the right one)

(12x +/- _____)(x +/- ____)

(6x +/- _____)(2x +/- ____)

(4x +/- ____)(3x +/- _____)

You know the factors of 15 are 1, 3, 5, and 15, but you know you probably won't be using 1 and 15. Plug 3 and 5 into each equation until it is equal to -15 and 11x. In this case, you will plug them into the last equation.

(4x - 3)(3x + 5)

You multiply the two inner numbers (-3 and 3x = -9x) and the two outer numbers (4x and 5= 20x) and add the -9x with the 20x to get 11x.

Then set each equation equal to zero to solve for x:

4x-3 = 0

3x + 5= 0

And I am hoping you can figure it out from there.

Answer 3

x^2 - 2x = 11x Subtract 11x from both sides

x^2 - 13x = 0 Factor

x(x - 13) = 0 Zero Product Property

x = 0

x - 13 = 0 Add 13 to both sides

x = 13

12x^2 - 15 = -11x Add 11x to both sides

12x^2 + 11x - 15 = 0 Factor

12x^2 - 9x + 20x - 15 = 0 Factor 12x^2 - 9x and 20x - 15

3x(4x - 3) + 5(4x - 3) = 0

(3x + 5)(4x - 3) = 0 Zero Product Property

3x + 5 = 0 Subtract 5 from both sides

3x = -5 Divide 3 from both sides

x = -5 / 3

4x - 3 = 0 Add 3 to both sides

4x = 3 Divide 4 from both sides

x = 3 / 4

Once you have come to your final answers, substitute your answers back into the orignal equation to check for any extraneous solutions.

Answer 4

x^2 - 2x = 11x

x^2 - 2x - 11x = 0

x^2 - 13x = 0

x (x - 13) = 0

x =0 or x = 13

12x^2 - 15 = -11x

12x^2 + 11x - 15 = 0

(4x-3)(3x+5) = 0

4x-3 = 0, x = 3/4

or

3x+5 = 0, x = -5/3

Answer 5

For the first, get zero on the right hand side by subtracting 11x:

x^2 - 13x = 0

Now, factor an x out:

x(x-13) = 0

When is that equal to zero? When one of the things being multiplied is zero.

So, if x=0 or x= +13, then the product will be zero.

Next one.

12x^2 +11x - 15 = 0 (I added 11x to each side to get the right hand side to zero. Very handy that right hand side being zero.)

So, we need a product of -180 (12 times 15) and a sum of positive 11.

I'm thinking.... 9 and 20 should do the trick.

Positive 20 and negative 9

12x^2 + 20x - 9x -15 (break the middle number down into the two "magic" numbers, and then factor two terms at a time, hoping for an equal residue...)

4x(3x + 5) -3(3x+5)

(4x-3)(3x+5) = 0

If:

x = 3/4 or x = -5/3

Answer 6

For the first quadratic equation, the goal is to arrange it into a standard form so that you can easily factor for the purpose of finding a value for x.  The general equation from above can be arranged into a standard equation such as: x^2 - 13x = 0, which is thus, factored into x(x - 13).  By letting this factored equation be set to 0 and solving for x yields, x(x  - 13) = 0.  Two solutions of this equation are x = 0, 13.  

For the second quadratic equation 12x^2 - 15 = -11x = 12x^2 + 11x - 15 = 0.  By factoring the equation, you have (4x - 3)(3x + 5) = 0.  Solving this equation yields a solution of x = -5/3, 3/4.

J.C

Answer 7

start by subtracting the 11x in the first problem from both sides

start by adding the 11x in the second problem from both sides...

sorry i wud help more but i dont get those weird symbols....the little arrow pointing up?????? sorry rewrite the prob and ill help moire

Answer 8

x^2 - 2x = 11x

x^2 - 13x = 0

x(x-13) = 0

x = 0, x = 13

12x^2 + 11x - 15 = 0

(4x - 3)(3x + 5) = 0

4x - 3 = 0; 4x = 3; x = 3/4

3x+5 = 0; 3x = -5; x = -5/3

Answer 9

1...

x^2 - 2x - 11x = 0

x^2 - 13x = 0

x(x - 13) = 0

x = 0 or x = 13

#2

12x^2 + 11x - 15 = 0

(4x - 3)(3x + 5) = 0

4x - 3 = 0   or    3x + 5 = 0

4x = 3    or      3x = -5

x = 3/4    or  x = -5/3  (ANSWER)

Take care,

David