Answer:
x = - 3 or x = 7
Step-by-step explanation:
Given
f(x) = x² - 4x + 6
If f(x) = 27, then equating gives
x² - 4x + 6 = 27 ( subtract 27 from both sides )
x² - 4x - 21 = 0 ← in standard form
Consider the factors of the constant term ( - 21) which sum to give the coefficient of the x- term ( - 4)
The factors are - 7 and + 3, since
- 7 × 3 = - 21 and - 7 + 3 = - 4, hence
(x - 7)(x + 3) = 0
Equate each factor to zero and solve for x
x + 3 = 0 ⇒ x = - 3
x - 7 = 0 ⇒ x = 7
