Question

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

x=−11+14−−√, −11−14−−√


x=11+14−−√, 11−14−−√


x=−11+315−−√, −11−315−−√


x=11+315−−√, 11−315−−√

Answer 1

x^2 − 22x + 1 = 15
⇒ x^2 − 22x − 14 = 0
Complete the square: x^2 − 22x = (x − 11)^2 − 121
So (x − 11)^2 − 121 − 14 = 0 ⇒ (x − 11)^2 = 135
x − 11 = ±√135 = ±3√15
Therefore x = 11 ± 3√15 (equivalently x = 11 ± √135).