Completing the Square

Completing the Square

How to solve quadratic equations by completing the square: example and its solution.

Example

Solve the given equation. x^2 + 8x - 5 = 0

Move the constant term -5 to the right side.

Change +8x to +2⋅x⋅4.

Write +42 on both sides.

Factor the left side by using the formula:
x2 + 2⋅x⋅4 + 42 = (x + 4)2.

Square root both sides.

Add ± in front of √21,
because both (√21)2 and (-√21)2 can be 21.

Move +4 to the right side.
Then x = -4 ± √21.