Question

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

x=11+√14, 11−√14

x equals 11 plus Start Root 14 End Root comma 11 minus Start Root 14 End Root

x=11+3√15, 11−3√15

x equals 11 plus 3 Start Root 15 End Root comma 11 minus 3 Start Root 15 End Root

x=−11+3√15, −11−3√15

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 negative 11 plus Start Root 14 End Root comma negative 11 minus Start Root 14 End Root

Answer 1

Start with x^2 − 22x + 1 = 15 ⇒ x^2 − 22x − 14 = 0.
Complete the square: (x − 11)^2 = x^2 − 22x + 121, so
(x − 11)^2 − 135 = 0 ⇒ (x − 11)^2 = 135 = 9·15.
Thus x − 11 = ±3√15, so x = 11 ± 3√15.

Answer: x = 11 + 3√15, 11 − 3√15.