Solve Quadratic Equations by Completing the Square: example 10.21

Solve $p^{2} - 18 p = −6$ 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 $x^{2} - 16 x = −16$ by completing the square.

How did it go?

The variable terms are on the left side.
Take half of $− 18$ and square it. $(\frac{1}{2} (− 18))^{2} = 81$
Add 81 to both sides.
Factor the perfect square trinomial as a binomial square.
Use the Square Root Property.
Simplify the radical.
Solve for p.
Rewrite to show two solutions.
Check.

The variable terms are on the left side.
Take half of $− 18$ and square it. $(\frac{1}{2} (− 18))^{2} = 81$
Add 81 to both sides.
Factor the perfect square trinomial as a binomial square.
Use the Square Root Property.
Simplify the radical.
Solve for p.
Rewrite to show two solutions.
Check.