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In the equation x+8=x(x+3), what is x?

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1 Answer

From the subject headings you know that this is going to have to be converted into a quadratic equation of the form

ax2 + bx + c = 0

So, using the equation you provided, distribute x on the right side

x*(x+3) = x2 + 3x

and then collect all of your terms on one side of the equation

x - x + 8 - 8 = x2 + 3x - x -8

0 = x2 + 2x - 8

The sign by the "c" term is negative and that indicates that when you factor this the two signs will be different from each other since only a positive and a negative number can multiply to give another negative.

So you''re looking at

(x + _ )(x - _ )

So, you want to look for factors of -8 that add together to equal the "b" term of 2.

Your choices are [-1,8] [1,-8] [2,-4] [-2,4]

Since -2 + 4 = 2 the last choice is the only one that makes sense, and your answer in factored form is then

(x + 4)(x - 2) = 0

But you're not done, in order for that equation to be correct then the values of x needed to equal to 0 are

x + 4 = 0 ===> x = -4

x -2 = 0  ===> x = 2

are your answers since they both satisfy the original equation. Plug them back into to check:

-4 + 8 = -4*(-4 + 3)

4 = -4*-1

4 = 4

and

2 + 8 = 2*(2 + 3)

10 = 2*5

10 = 10