Question

Solve for x by completing the square: x2 - 12x + 11 = 0

A.
(-11,0) and (1,0)
B.
(1,0) and (11,0)
C.
(0,1) and (0,-11)

Answer 1

B

Explanation:

x² - 12x + 11 = 0 ( subtract 11 from both sides )

x² - 12x = - 11

To complete the square

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

x² + 2(- 6)x + 36 = - 11 + 36

(x - 6)² = 25 ( take square root of both sides )

x - 6 = ±
`√(25)` = ± 5 ( add 6 to both sides )

x = 6 ± 5

Then

x = 6 - 5 = 1 ⇒ (1, 0 )

x = 6 + 5 = 11 ⇒ (11, 0 )