C. Solving Quadratic Equations by Factoring

Using the graph of a quadratic function to solve a quadratic equation is not necessarily the most efficient method. Another way to solve quadratic equations, more directly, is to use the factoring strategies reviewed earlier in this Unit.

As such, one method of solving a quadratic equation is to:

  • rearrange the equation so one side of the equal sign is zero
  • factor the quadratic expression on the other side of the equal sign
  • determine what value of the variable makes each factor equal to zero
  • verify the solutions by substituting them back into the original equation

Example 1

Solve .

This is a quadratic equation with one side equal to zero and it has already been factored. You can now determine which values of x make each factor equal to 0.

The solutions to the equation are 3 and .

Verify the solutions by substituting them back into the original equation.

For x = 3,

Left side
Right side
0

The two sides are equal, so 3 is a solution.

For ,

Left side
Right side
0

The two sides are equal, so is also a solution.