# Completing the square

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Give an example using either completing the square or the quadratic formula and explain each step as if you were teaching someone who had never used the method before.

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##### Solution Summary

An example, using either completing the square or the quadratic formula is give.

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A quadratic equation is a second-order polynomial equation in a single variable

ax² + bx + c = 0

where a is not equal to 0.

Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has two solutions. These solutions may be both real, or both complex.

The roots can be found by completing the square,

x² + (b/a)x = - (c/a)

Add b² / (4a²) to ...

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