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# Solving Quadratic Equations by Completing the Square

Objective Learn the technique of completing the square, and how to use this technique to solve quadratic equations and to verify the Quadratic Formula.

Completing the square is an important technique in working with quadratic equations. The technique is motivated by the simplest example of a quadratic equation, when the square of a variable is equal to a positive number.

## Taking the Square Root of Each Side

Example 1

Solve x 2 - 9.

Solution

To solve this equation, simply take the square root of each side.

You can also use this method to solve a quadratic equation in which the square of an expression of the form ( x - c ) is equal to a positive number.

Example 2

Solve ( x - 3) 2 = 16.

Solution

Again, take the square root of each side.

These examples show how to solve quadratic equations of the form ( x + k ) 2 = d or ( x + k ) 2 - d = 0. This is called completed square form. Quadratic equations that are not in this form can be rewritten using a technique called completing the square.