Solve Quadratic Equations by Completing the Square: example 10.24

Solve $(x - 3) (x + 5) = 9$ by completing the square.

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Solve $(c - 2) (c + 8) = 7$ by completing the square.

How did it go?


We multiply binomials on the left.
Add 15 to get the variable terms on the left side.
Take half of 2 and square it. $(\frac{1}{2} (2))^{2} = 1$
Add 1 to both sides.
Factor the perfect square trinomial as a binomial square.
Use the Square Root Property.
Solve for x.
Rewite to show two solutions.
Simplify.
Check. We leave the check for you!


We multiply binomials on the left.
Add 15 to get the variable terms on the left side.
Take half of 2 and square it. $(\frac{1}{2} (2))^{2} = 1$
Add 1 to both sides.
Factor the perfect square trinomial as a binomial square.
Use the Square Root Property.
Solve for x.
Rewite to show two solutions.
Simplify.
Check. We leave the check for you!