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Media4Math  Solving Quadratic Equations by Completing the Square

Completing the Square

In this example a quadratic equation is solved by completing the square. Two real solutions are found.

Review of completing the square:

The technique of completing the square allows you to solve a quadratic equation by rewriting it in a way to find the roots without using the quadratic formula. In the technique of completing the square a quadratic equation in standard form is rewritten as the square of a binomial.

ax2 + bx + c = 0

The simplest form to work with is when a = 1. In this case, you are looking for a binomial of the form (x + C)2, for some constant C. Completing the square involves arranging the expanded form (x + C)2 based on the given quadratic equation. In order to keep the quadratic equation balanced, it is necessary to add and subtract the same terms, as part of completing the square.

When a does not equal 1, then the technique of completing the square involves finding a binomial of the form (CX + D)2, for two constants C and D.

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