Question

| 1. What are the values of x in the equation x(x – 6) = 4(x + 6)?
(1) {-6,6} (2) {-12, 2} (3) {-2, 12} (4) {-6,0, 6}

Answer 1

Answer:

x = - 2, x = 12

Step-by-step explanation:

Given

x(x - 6) = 4(x + 6) ← distribute parenthesis on both sides

x² - 6x = 4x + 24 ← subtract 4x + 24 from both sides

x² - 10x - 24 = 0

Consider the factors of the constant term (- 24) which sum to give the coefficient of the x- term (- 10)

The factors are - 12 and + 2, since

- 12 × 2 = - 24 and - 12 + 2 = - 10, thus

(x - 12)(x + 2) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 12 = 0 ⇒ x = 12

x + 2 = 0 ⇒ x = - 2