Factoring and Completing the Square

Completing the Square

​Complete the square, then factor the trinomial.

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What is the "c" that will complete the square for $x^2-12x$ ?

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Factor the trinomial from the previous problem:

$x^2-12x$

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What is the "c" that will complete the square for $x^2+8x$ ?

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Factor the trinomial from the previous problem:

$x^2+8x$

PAUSE!!!

We are taking a quick break to practice getting "c" when completing the square. Grab a maze worksheet to match the correct "c" to complete the square.

Solve the equation using completing the square.

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Solve the following equation by completing the square:

$x^2-14x+?=\ -13+?$

What is the "c" that needs to be added to both sides?

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From the previous problem we have:

$\left(x-7\right)^2=?$

What is the ? on the right hand side?

Multiple Choice

Now that we have:

$$\left(x-7\right)^2=36$$

what do we need to do to BOTH sides now?

• Divide by 2

• Square root

• Add 7

Multiple Choice

How many solutions does your problem have?

• 0

• 1

• 2

• 3

Multiple Choice

What are your TWO solutions to the following equation?

$$x-7=\pm6$$

• 13, 1

• -13, 1

• -13, -1

• 13, -1

Multiple Choice

Solve the following by comleting the square:

$$3x^2-30x+22=0$$

• $$5+\sqrt{3},\ 5-\sqrt{3}$$

• $$19,\ -3$$

• $$-2+7\sqrt{2},\ -2-7\sqrt{2}$$

• $$-8+\sqrt{7},\ -8-\sqrt{7}$$