Answer:
x = 5 + sqrt(7) or x = 5 - sqrt(7)
Step-by-step explanation by completing the square:
Solve for x:
x^2 - 10 x + 26 = 8
Subtract 26 from both sides:
x^2 - 10 x = -18
Add 25 to both sides:
x^2 - 10 x + 25 = 7
Write the left hand side as a square:
(x - 5)^2 = 7
Take the square root of both sides:
x - 5 = sqrt(7) or x - 5 = -sqrt(7)
Add 5 to both sides:
x = 5 + sqrt(7) or x - 5 = -sqrt(7)
Add 5 to both sides:
Answer: x = 5 + sqrt(7) or x = 5 - sqrt(7)