How to Solve (and Factor) a Quadratic Equation with the Quadratic Formula
Understanding the Binomial Theorem
How to Perform Operations with Complex Numbers

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.

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

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

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

  4. Factor the left side.

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

  5. Take the square root of both sides.

  6. Solve.

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