Module 22.2

Solving Equationsby Completing The Square

How can you use completing the squareto solve a quadratic equation?

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Can this be solved as we have in the past?

Subtracting 3 from both side gives: 𝒙𝟐 − 𝟒𝒙 − 𝟑 = 𝟎

But are there 2 numbers that multiply to –3 and add up to –4? No.

So we need a new method to solve it.

Given

Completing the square is a process of rewriting a quadratic expression as a

perfect square trinomial so that it can be solved by taking square roots.

First: To complete the square, add 𝒃𝟐

𝟒𝒂

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4

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