Michael B. answered 04/10/13
Seasoned and experienced tutor with extensive science background
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