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To complete the square of a binomial such as x² + 12x means to add a third term that will form a perfect square trinomial. To complete the square of a binomial in the form x² + bx, first take half of b and square it. Then add the square to x² + bx. The result is a perfect square trinomial.

You can use the process of completing the square to solve quadratic equations. Be sure that the quadratic equation is written in the form ax² + bx + c = 0   before starting this process.

Examples:
a.) Complete the square:
x² + 12x
( 1/2 * 12 )² = 6² = 36
add 36.
answer: x² + 12x

b.) Find the solution set of x² - 2x - 15 = 0 by completing the square:
x² - 2x = 15
x² - 2x + 1 = 15 + 1     [ add   (1/2 * -2)² = -1² = 1   ]
( x - 1 )² = 16
x + 1 = 4
x = 1 + 4
answer: x = 5