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 Depdendent Variable

 Number of equations to solve: 23456789
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 Dependent Variable

 Number of inequalities to solve: 23456789
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Here we apply the method for completing the square to the general quadratic equation to get a formula for the solutions to any quadratic equation.

## Developing the Formula

Assume a is positive for now, and divide each side by a:

 = 0 Subtract from each side.

One-half of is , and squared is :

Factor the left-hand side and get a common denominator for the right-hand side:

 Even-root property x x

We assumed a was positive so that would be correct. If a is negative, then , and we get

However, the negative sign can be omitted in -2a because of the Â± symbol preceding it. For example, the results of 5 Â± (-3) and 5 Â± 3 are the same. So when a is negative, we get the same formula as when a is positive. It is called the quadratic formula.