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Completing the Square

November 22, 2022 by sastry

Completing the Square

An equation in which one side is a perfect square trinomial can be easily solved by taking the square root of each side.
Consider the example at the right:

Complete-the-Square-1

It is this method of solution that is the basis of a process called “completing the square”.

Consider the equation: .

Complete-the-Square-2

Our solution strategy will be to “force” a perfect square trinomial of the form

Complete-the-Square-3

on the left hand side of the equation.
This method of “forcing” the existence of a perfect square trinomial is completing the square.

Steps for Completing the Square:

Complete-the-Square-4

Examples: Solve each example by completing the square.

Complete-the-Square-5
Complete-the-Square-6

Filed Under: Mathematics

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