How do you factor x^2+ 11x = 180?

1 Answer
May 24, 2015

First subtract 180 from both sides to get:

x^2+11x-180 = 0

Noticing that the coefficient of x^2 is 1 and the signs of the other two coefficients, this may factorize as:

(x+a)(x-b) = x^2+(a-b)x-ab with a > 0, b > 0, a-b = 11 and ab = 180.

180 = 20 xx 9 and 11 = 20 - 9

So we can let a=20 and b=9 to get:

x^2+11x-180 = (x+20)(x-9)

Hence x^2+11x=180 has solutions x=-20 and x=9