Question

Question is in the picture.

Answer 1

x = 3 ± 2
`√(6)`

Explanation:

x² - 6x = 15

to complete the square on the left side

add ( half the coefficient of the x- term )² to both sides

x² + 2(- 3)x + 9 = 15 + 9

(x - 3)² = 24 ( take square root of both sides )

x - 3 = ±
`√(24)` = ±
`√(4(6))` = ± (
`√(4)` ×
`√(6)` ) = ± 2
`√(6)`

add 3 to both sides

x = 3 ± 2
`√(6)`

then

x = 3 - 2
`√(6)` , x = 3 + 2
`√(6)`