# Lesson 12

Completing the Square (Part 1)

• Let’s learn a new method for solving quadratic equations.

### Problem 1

Add the number that would make the expression a perfect square. Next, write an equivalent expression in factored form.

1. $$x^2 - 6x$$
2. $$x^2 + 2x$$
3. $$x^2 + 14x$$
4. $$x^2 - 4x$$
5. $$x^2 + 24x$$

### Problem 2

Mai is solving the equation $$x^2 + 12x = 13$$. She writes:

\displaystyle \begin{align} x^2 + 12x &= 13\\ (x + 6)^2 &= 49\\ x &= 1 \text { or } x = \text- 13\\ \end{align}\\

Jada looks at Mai’s work and is confused. She doesn’t see how Mai got her answer.

Complete Mai’s missing steps to help Jada see how Mai solved the equation.

### Problem 3

Match each equation to an equivalent equation with a perfect square on one side.

### Problem 4

Solve each equation by completing the square.

$$x^2-6x+5=12$$

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

$$11=x^2+4x-1$$

$$x^2-18x+60=\text-21$$

### Problem 5

Rewrite each expression in standard form.

1. $$(x+3)(x-3)$$
2. $$(7+x)(x-7)$$
3. $$(2x-5)(2x+5)$$
4. $$(x+\frac18)(x-\frac18)$$
(From Unit 7, Lesson 8.)

### Problem 6

To find the product $$203 \boldcdot 197$$ without a calculator, Priya wrote $$(200+3)(200-3)$$. Very quickly, and without writing anything else, she arrived at 39,991. Explain how writing the two factors as a sum and a difference may have helped Priya.

(From Unit 7, Lesson 8.)

### Problem 7

A basketball is dropped from the roof of a building and its height in feet is modeled by the function $$h$$.

Here is a graph representing $$h$$.

A:

When $$t=0$$ the height is 0 feet.

B:

The basketball falls at a constant speed.

C:

The expression that defines $$h$$ is linear.

D:

The expression that defines $$h$$ is quadratic.

E:

When $$t=0$$ the ball is about 50 feet above the ground.

F:

The basketball lands on the ground about 1.75 seconds after it is dropped.

(From Unit 6, Lesson 5.)

### Problem 8

A group of students are guessing the number of paper clips in a small box.

The guesses and the guessing errors are plotted on a coordinate plane.

What is the actual number of paper clips in the box?​​​​​​

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(From Unit 4, Lesson 13.)