Completing the square

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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 ...