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 Number of inequalities to solve: 23456789
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Quadratic equations are of the form ax + bx + c = 0, where a 0

Quadratics may have two, one, or zero real solutions .

## 1. Completing the Square

If the quadratic equation is of the form ax + bx + c = 0, where a 0 and the quadratic expression is not factorable, try completing the square.

Example: x + 6x - 11 = 0

**Important: If a 1, divide all terms by “a” before proceeding to the next steps.

 Move the constant to the right side x + 6x = 11 Find half of b, which means Find : 3 = 9 Add to both sides of the equation x + 6x + 9 = 11 + 9 Factor the quadratic side (x + 3)(x + 3) = 20 (which is a perfect square because you just made it that way!) Then write in perfect square form (x + 3)= 20 Take the square root of both sides Solve for x Simplify the radical This represents the exact answer. Decimal approximations can be found using a calculator.