Activity
Han and Jada solved the same quadratic equation with different methods. Here they are:
Han's Method | Jada's Method |
|
|
Work with a partner to solve these equations. For each equation, one partner solves with Han's method, and the other partner solves with Jada's method. Make sure both partners get the same solutions to the same equation. If not, work together to find your mistakes.
Enter the solutions to this equation.
Compare your answer:
and
Enter the solutions to this equation.
Compare your answer:
and
Compare your answer:
or and or
Enter the solutions to this equation.
Compare your answer:
and
Video: Learning About Solving Multi Step Quadratic Equations Using Perfect Squares
Watch the following video to learn more about solving multi step quadratic equations using perfect squares.
Self Check
Additional Resources
Two Ways to Solve Quadratic Equations
In the activity, Han and Jada used two different methods for solving a quadratic equation, using the distributive property and the square root property.
Using the Distributive Property to Solve Quadratic Equations
How to Solve a Quadratic Equation Using the Distributive Property:
Step 1 - Isolate the quadratic term and make its coefficient 1.
Step 2 - Rewrite the term so the binomial is multiplied by itself.
Step 3 - Use the distributive property or FOIL.
Step 4 - Combine like terms so that the equation is set equal to 0.
Step 5 - Factor.
Step 6 - Set each factor equal to 0.
Step 7 - Solve.
Step 8 - Check the solutions.
Example
Solve
Step 1 - Isolate the quadratic term (divide by 4).
Step 2 - Rewrite the term so the binomial is multiplied by itself.
Step 3 - Use the distributive property or FOIL.
Step 4 - Combine like terms so that the equation is set equal to 0.
Step 5 - Factor.
Step 6 - Set each factor equal to 0.
,
Step 7 - Solve.
Step 8 - Check the solutions.
Try it
Try It: Using the Distributive Property to Solve Quadratic Equations
Use the distributive property to solve .
Here is how to solve the quadratic equation using the distributive property.
Step 1 - Isolate the quadratic term (divide by 3).
Step 2 - Rewrite the term so the binomial is multiplied by itself.
Step 3 - Use the distributive property or FOIL.
Step 4 - Combine like terms so that the equation is set equal to 0.
Step 5 - Factor.
Step 6 - Set each factor equal to 0.
or
Step 7 - Solve.
Step 8 - Check the solutions.
If , then
or or
How to Solve a Quadratic Equation Using the Square Root Property:
Step 1 - Isolate the quadratic term and make its coefficient one.
Step 2 - Use the square root property. Take the square root of both sides of the equation and remember the "plus or minus."
Step 3 - Rewrite the equation as two equations.
Step 4 - Solve each equation.
Step 5 - Check the solutions.
Example
Solve
Step 1 - Isolate the quadratic term (divide by 4).
Step 2 - Use the square root property.
Step 3 - Rewrite the equation as two equations.
Step 4 - Solve each equation.
Step 5 - Check the solutions.
Try it
Try It: Using the Square Root Property to Solve Quadratic Equations
Use the square root property to solve .
Here is how to solve the quadratic equation using the square root property:
Step 1 - Isolate the quadratic term (divide by 3).
Step 2 - Use the square root property.
Step 3 - Rewrite the equation as two equations.
Step 4 - Solve each equation.
Step 5 - Check the solutions.