Question

Solve the equation 4n2 − 16n − 84 = 0 by completing the square.

n = 7; n = −3
n = −8; n = 4
n = −7; n = 12
n = −6; n = 2

Answer 1

4n² - 16n - 84 = 0

Multiply both sides by 1/4 :

n² - 4n - 21 = 0

Add 21 to both sides:

n² - 4n = 21

Complete the square by adding 4 to both sides:

n² - 4n + 4 = 25

(n - 2)² = 25

Solve for n :

n - 2 = ± √25

n - 2 = ± 5

n = 2 ± 5

Then n = 2 + 5 = 7 or n = 2 - 5 = -3.