Solve for x:
x^2 - 8 x + 14 = 0
Solve the quadratic equation by completing the square.
Subtract 14 from both sides:
x^2 - 8 x = -14
Take one half of the coefficient of x and square it, then add it to both sides.
Add 16 to both sides:
x^2 - 8 x + 16 = 2 [THIS STEP IS THE SECOND ONE OF YOUR 4 CHOICES]
Factor the left hand side.
Write the left hand side as a square:
(x - 4)^2 = 2
Eliminate the exponent on the left hand side.
Take the square root of both sides:
x - 4 = sqrt(2) or x - 4 = -sqrt(2)
Look at the first equation: Solve for x.
Add 4 to both sides:
x = 4 + sqrt(2) or x - 4 = -sqrt(2)
Look at the second equation: Solve for x.
Add 4 to both sides:
x = 4 + sqrt(2) or x = 4 - sqrt(2)
