Question

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

Answer 1

Answer:

x = 5 ± $\sqrt{7}$

Step-by-step 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 = ± $\sqrt{7}$ ( add 5 to both sides )

x = 5 ± $\sqrt{7}$ ← exact solutions

Answer 2

Answer:

$x=5-\sqrt{7}\\x=5 +\sqrt{7}$

Step-by-step explanation:

$x^2-10x+26-8=0\\x^2-10x+18=0\\x=\frac{10+2\sqrt{7} }{2\\}\\x=\frac{10-2\sqrt{7} }{2}\\x=5+\sqrt{7}\\x=5-\sqrt{7}$