Solve Quadratic Equations by Completing the Square: example 10.20

Solve $x^{2} + 4 x = −21$ 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 $y^{2} - 10 y = −35$ by completing the square.

How did it go?

The variable terms are on the left side.
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.
We cannot take the square root of a negative number.		There is no real solution.

The variable terms are on the left side.
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.
We cannot take the square root of a negative number.		There is no real solution.