Answer:
x = - 6 , x = 7
Step-by-step explanation:
given
x² - x - 42 = 0
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
x² - x - 42 = (x - 7)(x + 6) and so
(x - 7)(x + 6) = 0
Equate each factor to zero and solve for x
x - 7 = 0 ⇒ x = 7
x + 6 = 0 ⇒ x = -6
Solutions are x = - 6, x = 7
