Algebra
Intermediate

Completing the Square

Rewrite a quadratic as a perfect square plus a constant.

Formula

x2+bx=(x+b2)2−b24x^2 + bx = \left(x+\frac{b}{2}\right)^2 - \frac{b^2}{4}

Variables

bLinear coefficient

Example

x²+6x = (x+3)²-9

Did You Know?

Completing the square is the ancient geometric trick, dating to Babylon, that eventually produced the quadratic formula.

quadratic