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Completing the Square

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Completing the Square

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    1. Completing the Square Section 5.5

    2. Factor the following:

    3. What do you notice about each of those problems? The last number is a perfect square. The last number is always positive. Its square root is 1/2 the middle (“b”) term. The answer can be written two ways.

    4. Use this information to find “c”, then factor. THINK: 1/2 the “b” term squared.

    5. What you’ve just done is called “completing the square” and here’s why we might need it:

    6. We can’t factor because there are no factors of 2 that have a difference of 2.

    7. The -2 at the back is causing problems so we will move it across the equal sign and complete the square. Consider the problem and move the -2 (constant) to the right. We’ll have to add something so that we can complete the square we’ll call it “c”. But it must be added to both sides to keep the equation balanced. We’ll find “c” just as we did before, but add it to both sides, then factor the left.

    8. Now solve the equation. Rewrite the equation. Square root both sides. Then finish.

    9. Try this one. Move the last term to the right. Figure 1/2 of “b” then square. Factor the left and combine terms on the right. Square root each side and solve.

    10. You try

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