Solving Quadratics by the Quadratic Formula

The following represents any quadratic equation:

ax 2 + bx + c = 0

This can be solved using the completing the square method to produce a formula that can then be applied to all quadratic equations.

Example 1

Solve ax 2 + bx + c = 0, a ≠ 0, for x by using the completing the square method.

ax 2 + bx + c = 0

Get the coefficient of the squared term to be 1.

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Isolate the variable terms.

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Complete the square.

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Apply the square root property.

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This last result is referred to as the quadratic formula. Remember, the quadratic formula can be used to solve all quadratic equations.

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Example 2

Solve 2 x 2 – 3 x + 4 = 0 by applying the quadratic formula.

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Note that this is the same problem solved in Example by completing the square. Here, however, it is solved by direct application of the quadratic formula.