Question

Find the zeros of y=x2 - 4x - 9 by completing the square.

Answer 1

x = 2 ±
`√(13)`

Explanation:

Given

y = x² - 4x - 9

To find the zeros, set y = 0, that is

x² - 4x - 9 = 0 ( add 9 to both sides )

x² - 4x = 9

To complete the square

add ( half the coefficient of the x- term)² to both sides

x² + 2(- 2)x + 4 = 9 + 4, that is

(x - 2)² = 13 ( take the square root of both sides )

x - 2 = ±
`√(13)` ( add 2 to both sides )

x = 2 ±
`√(13)` ← exact solutions