Solve Quadratic Equations by Completing the Square: example 10.22

Solve $x^{2} + 10 x + 4 = 15$ 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 $a^{2} + 4 a + 9 = 30$ by completing the square.

How did it go?

The variable terms are on the left side.
Subtract $4$ to get the constant terms on the right side.
Take half of 10 and square it. $(\frac{1}{2} (10))^{2} = 25$
Add 25 to both sides.
Factor the perfect square trinomial as a binomial square.
Use the Square Root Property.
Simplify the radical.
Solve for x.
Rewrite to show two equations.
Solve the equations.
Check.

The variable terms are on the left side.
Subtract $4$ to get the constant terms on the right side.
Take half of 10 and square it. $(\frac{1}{2} (10))^{2} = 25$
Add 25 to both sides.
Factor the perfect square trinomial as a binomial square.
Use the Square Root Property.
Simplify the radical.
Solve for x.
Rewrite to show two equations.
Solve the equations.
Check.