Complete the Square

Find the value that completes the square and then rewrite as a perfect square.

a² - 40a + ____

• 1600; (a - 20)²

• -20; (a - 20)²

• 81; (a - 9)²

• 400; (a - 20)²

Answer explanation

Divide -40 by 2. Square it for the first answer. Second answer is (a plus first result).

Solve. You might want to complete the square.

Answer explanation

Do 14/2. Then square it.
Add that to both sides.
Rewrite the left side as (x + (14/2))^2
Take the square root of both sides.
Remember to use +- square root on right side.
Now, solve for x.
You should have two answers.

Find the value that completes the square.
x2 + 4x + ___

Answer explanation

Divide +4 by 2.

Answer explanation

Answer is (x plus result)^2.

Solve the equation by completing the square.

• A

• B

• C

• D

Answer explanation

Subtract 20 from both sides.

Do +6/2. Then square it.

Add that to both sides.

Rewrite the left side as (x + (+6/2))^2

Take the square root of both sides.

Remember to use +- square root on right side.

Now, solve for x.

You should have two answers.

Solve. You might want to complete the square. Write just the answers without "x".

Answer explanation

Add 11 to both sides.
Do -4/2. Then square it.
Add that to both sides.
Rewrite the left side as (x + (-4/2))^2
Take the square root of both sides.
Remember to use +- square root on right side.
Now, solve for x.
You should have two answers.

Answer explanation

Subtract 8x from both sides.

Do -8/2. Then square it.

Add that to both sides.
Rewrite the left side as (x + __)^2
Take the square root of both sides.
Remember to use +- square root on right side.
Now, solve for x.
You should have two answers.

Did you take the square root of a negative number?

Answer explanation

Do b/2. Then square it.

Add that to both sides.
Rewrite the left side as (x + __)^2
Take the square root of both sides.
Remember to use +- square root on right side.
Now, solve for x.
You should have two answers.

Did you take the square root of a negative number?

Answer explanation

Subtract 45 from both sides.

Subtract 3x from both sides.

Do b/2. Then square it.

Add that to both sides.
Rewrite the left side as (x + __)^2
Take the square root of both sides.
Remember to use +- square root on right side.
Now, solve for x.
You should have two answers.

Did you take the square root of a negative number?

Answer explanation

Subtract 3 from both sides.

Subtract 6x from both sides.

Do b/2. Then square it.

Add that to both sides.
Rewrite the left side as (x + __)^2
Take the square root of both sides.
Remember to use +- square root on right side.
Now, solve for x.
You should have two answers.

Did you take the square root of a negative number?