Quadratic Formula:

Several quadratic equations cannot readily be solved through either of the two techniques already elaborate (taking the square roots or factoring).  For instance, the quadratic equation x2 - 6x + 4 = 0 is not a pure quadratic and, thus, cannot be solved by taking the square roots. Additionally, the left-hand side of the equation cannot readily be factored.  The Quadratic Formula is a third technique for solving quadratic equations. It can be used to find out the roots of any quadratic equation.

Equation 8 is the Quadratic Formula.  It states in which the two roots of a quadratic equation written in common form, ax² + bx + c = 0, are equal to x =   and . The Quadratic Formula should be committed to memory since it is such a useful tool for solving quadratic equations.

There are three steps in solving a quadratic equation using the Quadratic Formula.

Step 1. Write the equation in general forms.

Step 2. Substitute the values for a, b, and c into the Quadratic Formula and solve for x.

Step 3. Check the roots in the original equation.