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2. Quadratic Equations
Chapter 11

3. 11 Quadratic Equations 11.1 Review of Solving Equation by Factoring
11.2 The Square Root Property and Completing the Square
11.3 The Quadratic Formula
Putting It All Together
11.4 Equations in Quadratic Form
11.5 Formulas and Applications

4. Four Methods for Solving Quadratic Equations
11.1
Review of Solving Equations by Factoring
In section 7.5, we learned how to solve quadratic equations by factoring. We will
Not be able to solve all quadratic equations by factoring, however. Therefore, we
Need to learn other methods. In this chapter, we will discuss the following four
Methods for solving quadratic
Four Methods for Solving Quadratic Equations
Factoring
Square root property
Completing the square
Quadratic formula
1. Review How to Solve a Quadratic Equation by Factoring

5. Solve by factoring. Example 1
Solution
Step 1: Write equation in standard form
Subtract 10 on both sides.
Simplify.
Step 2: Factor expression.
Factor.
Set each factor equal to 0.
Solve. or

6. Solve by factoring. Example 2
Solution
Step 1: Write equation in standard form
One side of the equation must equal zero in order to use the zero product rule.
Multiply both factors.
Gather like terms on one side of equation.
Step 2: Factor expression.
Factor.
Set each factor equal to 0.
Solve. or
The solution set is { -1, 8}.

7. Solve by factoring. Example 3
Solution
Although this is a cubic equation and not quadratic, we can solve it by factoring.
Get zero on one side of the equal sign.
Factor out x.
Factor
Set each factor equal to zero.
Solve.
The check is left to the student.
The solution set is