How to Solve a Quadratic Equation by Completing the Square

You can solve quadratic equations by completing the square. Completing the square involves creating a perfect square trinomial from the quadratic equation, and then solving that trinomial by taking its square root.

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  1. Put the x-squared and the x terms on one side and the constant on the other side.

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  2. Divide both sides by the coefficient of x-squared (unless, of course, it’s 1).

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  3. Take half of the coefficient of x, square it, then add that to both sides.

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  4. Factor the left side.

    Notice that the factor always contains the same number you found in Step 3 (–4 in this example).

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  5. Take the square root of both sides.

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  6. Solve.

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