Answer:
x = 4 + sqrt(2) or x = 4 - sqrt(2)
Step-by-step explanation by completing the square:
Solve for x:
x^2/2 - 4 x + 7 = 0
Multiply both sides by 2:
x^2 - 8 x + 14 = 0
Subtract 14 from both sides:
x^2 - 8 x = -14
Add 16 to both sides:
x^2 - 8 x + 16 = 2
Write the left hand side as a square:
(x - 4)^2 = 2
Take the square root of both sides:
x - 4 = sqrt(2) or x - 4 = -sqrt(2)
Add 4 to both sides:
x = 4 + sqrt(2) or x - 4 = -sqrt(2)
Add 4 to both sides:
Answer: x = 4 + sqrt(2) or x = 4 - sqrt(2)
