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.

Isolate the variable terms.

Complete the square.

Apply the square root property.

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

##### Example 2

Solve 2 *x* ^{2} – 3 *x* + 4 = 0 by applying the quadratic formula.

Note that this is the same problem solved in Example