Question

Complete the square to solve the following quadratic equation: x^2−22x+1=15
.(1 point)
Responses

x=−11+315−−√, −11−315−−√
x equals negative 11 plus 3 Start Root 15 End Root comma negative 11 minus 3 Start Root 15 End Root

x=11+14−−√, 11−14−−√
x equals 11 plus Start Root 14 End Root comma 11 minus Start Root 14 End Root

x=11+315−−√, 11−315−−√
x equals 11 plus 3 Start Root 15 End Root comma 11 minus 3 Start Root 15 End Root

x=−11+14−−√, −11−14−−√
x equals negative 11 plus Start Root 14 End Root comma negative 11 minus Start Root 14 End Root

Answer 1

x^2 − 22x + 1 = 15
x^2 − 22x = 14
(x − 11)^2 − 121 = 14
(x − 11)^2 = 135 = 9·15
x − 11 = ±3√15
x = 11 ± 3√15

So the correct choice is x = 11 + 3√15, 11 − 3√15.