For what values of x is x2 + 2x = 24 true?

x = - 6, x = 4

Step-by-step explanation:

Given

x² + 2x = 24 ( subtract 24 from both sides )

x² + 2x - 24 = 0

To factorise the quadratic

Consider the factors of the constant term (- 24) which sum to give the coefficient of the x- term (+ 2)

The factors are + 6 and - 4, since

6 × - 4 = - 24 and 6 - 4 = + 2, hence

(x + 6)(x - 4) = 0

Equate each factor to zero and solve for x

x + 6 = 0 ⇒ x = - 6

x - 4 = 0 ⇒ x = 4