Question

(x+4)^2=18. (x+4)(x+4)-18= x^2+8x-2=0. (x )(x )I have no idea how to factor this because no factors of two will add up to 48. Can you offer an explanation and tips on factoring this sort of question?

Answer 1

As you can see this is not factorable in your head or obvious so we have to use the Quadratic Formula:

for Ax^2 + Bx + C = 0

x = ( -B / 2 A ) + or - ( sqrt (B ^ 2 - 4 x A x C) ) / 2 A

So A = 1, B = 8, C = -2

-8/ 2 + or - sqrt( 64- (4 x 1 x -2)) / 2
-4 + or - Sqrt( 72 ) / 2
-4 + or - 6 sqrt (2) / 2
-4 + or - 3 sqrt (2)

x = -4 + 3 sqrt (2) and -4 - Sqrt(2)