Solve Quadratic Equations by Completing the Square: example 10.25

Solve $3 x^{2} - 12 x - 15 = 0$ 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 $2 m^{2} + 16 m - 8 = 0$ by completing the square.

How did it go?


Factor out the greatest common factor.
Divide both sides by 3 to isolate the trinomial.
Simplify.
Subtract 5 to get the constant terms on the right.
Take half of 4 and square it. $(\frac{1}{2} (4))^{2} = 4$
Add 4 to both sides.
Factor the perfect square trinomial as a binomial square.
Use the Square Root Property.
Solve for x.
Rewrite to show 2 solutions.
Simplify.
Check.


Factor out the greatest common factor.
Divide both sides by 3 to isolate the trinomial.
Simplify.
Subtract 5 to get the constant terms on the right.
Take half of 4 and square it. $(\frac{1}{2} (4))^{2} = 4$
Add 4 to both sides.
Factor the perfect square trinomial as a binomial square.
Use the Square Root Property.
Solve for x.
Rewrite to show 2 solutions.
Simplify.
Check.