If f (x) = x^2 - 4 (x) + 6, find x if f (x) = 27

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