Question

Enter the correct answer in the box. Solve the equation by completing the square. x^2 − 10x + 26 = 8

Answer 1

x = 5 ±
`√(7)`

Explanation:

Given

x² - 10x + 26 = 8 ( subtract 26 from both sides )

x² - 10x = - 18

To complete the square

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

x² + 2(- 5)x + 25 = - 18 + 25

(x - 5)² = 7 ( take the square root of both sides )

x - 5 = ±
`√(7)` ( add 5 to both sides )

x = 5 ±
`√(7)` ← exact solutions

Answer 2

`x=5-√(7)\\x=5 +√(7)`

Explanation:

`x^2-10x+26-8=0\\x^2-10x+18=0\\x=(10+2√(7) )/(2\\)\\x=(10-2√(7) )/(2)\\x=5+√(7)\\x=5-√(7)`