Question 1121300
the quadratic equation is x^2 - 3x - 108 = 0


108 / 2 = 54
54 - 2 is not equal to 3.


108 / 3 = 36
36 - 3 is not equal to 3.


108 / 6 = 18
18 - 6 is not equal to 3


108 / 9 = 12
12 - 9 is equal to 3, therefore this combination should work.


since the constant term is negative, then it's going to be 12 * -9 or it's going to be 9 * -12.


either one will get you -108.


since the middle term is negative, then it can't be 12 - 3 becausee that's positive.


it has to be 9 - 12 = -3.


therefore the factors have to be (x - 12) * (x + 9).


when you multiply these factors out, you get:


(x - 12) * (x + 9) = x^2 + 9x - 12x - 108


combine like terms to get x^2 - 3x - 108.


either one of the factors have to be equal to 0, or both have to be equal to 0.


when x - 12 = 0, solve for x to get x = 12.


when x + 9 = 0, solve for x to get x = -9


if the values of x are good, then x^2 - 3x - 108 should be equal to 0 when you replace x with either 12 or -9.


when x = 12, x^2 - 3x - 108 = 12^2 - 3*12 - 108 = 144 - 36 - 108 = 0.


when x = -9, x^2 - 3x - 108 = (-9)^2 -3*-9 - 108 = 81 + 27 - 108 = 0.


both solutions are good.


not sure if that's what you want, but that's what you get.


here's what the solution looks like on a graph.


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