1. Solving Equations That Lead to Quadratic Equations There are several methods one can use to solve a quadratic equation. Sometimes we are called upon to solve an equation that is not quadratic, but the solution process leads to a quadratic equation. Two examples of this will be given. Recall that a quadratic equation is an equation that can be simplified into the form …

2. Example 1: Multiply every term by the common denominator to yield Simplify Solve the equation

3. Note that this is a quadratic equation. Further simplifying leads to …

4. Use the quadratic formula to complete the problem.

5. Note that neither of these solutions makes a denominator in the original rational equation zero, so both solutions are valid. Note also that we started with a rational equation, but the solution process lead to a quadratic equation.

6. Example 2: Square both sides … Simplify Solve the equation

7. Factor and solve.

8. Note that this solution checks in the original equation … Here we started with a radical equation, but the solution process lead to a quadratic equation.