Question

Complete the square to solve the following quadratic equation: x2−22x+1=15

Answer 1

x^2 − 22x + 1 = 15
=> x^2 − 22x − 14 = 0

Complete the square: add 121 to both sides (since (22/2)^2 = 11^2 = 121)
=> x^2 − 22x + 121 = 135
=> (x − 11)^2 = 135

So x − 11 = ±√135 = ±3√15, hence
x = 11 ± 3√15 (≈ 22.6189 or −0.6189).