Use the zero product property to find the solutions to the equation x^2 + x - 30 = 12. x = - 7 or x = 6 x = - 7 or x = - 6 x = - 6 or x = 7 x = 6 or x = 7

x = - 7 or x = 6

Step-by-step explanation:

given

x² + x - 30 = 12 (subtract 12 from both sides)

x² + x - 42 = 0 ← in standard form

To factorise, consider the factors of the constant term ( - 42) which sum to give the coefficient of the x - term ( + 1)

The factors are + 7 and - 6, since

+ 7 * - 6 = - 42 and + 7 - 6 = + 1, hence

(x + 7) (x - 6) = 0

Equate each factor to zero and solve for x (zero product property)

x + 7 = 0 ⇒ x = - 7

x - 6 = 0 ⇒ x = 6

x2 + x - 30 = 12

x2 + x - 42 = 0

(x + 7) (x - 6) = 0

By zero product property, either (x + 7) = 0 or (x - 6) = 0.

So x = - 7/6.