Solve x^2 + 5x - 14 = 0

x = - 7, x = 2

Step-by-step explanation:

Given

x² + 5x - 14 = 0

Consider the factors of the constant term ( - 14) which sum to give the coefficient of the x - term ( + 5)

The factors are + 7 and - 2, since

7 * - 2 = - 14 and 7 - 2 = + 5, thus

(x + 7) x - 2) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 7 = 0 ⇒ x = - 7

x - 2 = 0 ⇒ x = 2

x = - 7, x = 2