Completing the Square

Solving Quadratics by
Completing the Square

use the quadratic formula.

complete the square.

When a quadratic isn't easily factored:

​How to complete the square:

Step 2:
Find the number that will
"complete the square."

Math Response

Find the number that

will complete the square.

$$x^2+6x=-2$$

Type answer here

Correct Answer: 9

Deg^°

Rad

Math Response

Find the number that

will complete the square.

$$x^2+10x=4$$

Type answer here

Correct Answer: 25

Deg^°

Rad

Math Response

Find the number that

will complete the square.

$$x^2-2x=8$$

Type answer here

Correct Answer: 1

Deg^°

Rad

Math Response

Find the number that

will complete the square.

$$x^2+\frac{1}{2}x=-3$$

Type answer here

Correct Answer: \frac{1}{16}

Deg^°

Rad

Back to the example:

Step 3:
Now the left side is a Perfect Square Trinomial, factor it!

Step 4:

Take the square root of each side.

Finish solving for x.

Math Response

Practice the first step:

Rewrite the quadratic!

$$x^2+14x-33=0$$

Type answer here

Correct Answer: x^2+14x=33

Deg^°

Rad

Math Response

What number will be added to both sides of the equation to complete the square?

$$x^2+14x=33$$

Type answer here

Correct Answer: 49

Deg^°

Rad

Multiple Choice

Factor the Perfect Square Trinomial.

$$x^2+14x+49$$

• $$\left(x+7\right)\left(x-7\right)$$

• $$\left(x+7\right)^2$$

• $$\left(x-7\right)^2$$

• $$\left(x+49\right)^2$$

Multiple Choice

Solve for x.

$$\left(x+7\right)^2=82$$

• $$7\pm\sqrt[]{82}$$

• $$-14\pm\sqrt[]{82}$$

• $$-7\pm\sqrt[]{82}$$

• $$82\pm\sqrt[]{7}$$

On paper, show the steps to complete the square and solve for x.

On paper, show the steps to complete the square and solve for x.