1. (x – 6)2 = 9 Factor the trinomial.
Completing the Square
Lesson 5-7
Additional Examples
Solve x2 – 12x + 36 = 9.
x2 – 12x + 36 = 9
(x – 6)2 = 9 Factor the trinomial.
x – 6 = ±3 Find the square root of each side.
x – 6 = 3 or x – 6 = –3 Solve for x.
x = 9 or
x = 3

2. Find the missing value to complete the square: x2 + 20x + .
Completing the Square
Lesson 5-7
Additional Examples
Find the missing value to complete the square: x2 + 20x
= = 100 Find Substitute 20 for b. b 2 20
x2 + 20x Complete the square.

3. x2 + 4x = –1 Rewrite so all terms containing x are on one side.
Completing the Square
Lesson 5-7
Additional Examples
Solve x2 + 4x + 1 = 0. 4 2
= 4 Find 2 b 2 2
x2 + 4x = –1 Rewrite so all terms containing x are on one side.
x2 + 4x + 4 = –1 + 4 Complete the square by adding 4 to each side.
(x + 2)2 = 3 Factor the perfect square trinomal.
x + 2 = ± 3 Find the square root of each side.
x = –2 ± 3 Solve for x.

4. (continued) Check: (–2)2 – 2(–2 3) + ( 3)2 – 8 – 4 3 + 1
Completing the Square
Lesson 5-7
Additional Examples
(continued)
Check:
(–2)2 – 2(–2 3) + ( 3)2 – 8 –
(– )2 + 4(– ) + 1
x2 + 4x + 1
0 = 0
4 – –
(4 + 3 – 8 + 1) + (– )
(–2)2 + 2(–2 3) + ( 3)2 + (–8)
(–2 – 3)2 + 4(–2 – ) + 1
– 8 –
(4 + 3 – 8 + 1) + ( – )

5. Rewrite so all terms containing x are on one side.
Completing the Square
Lesson 5-7
Additional Examples
Solve x2 + 6x + 12 = 0. 6 2 2 b 2 2
= 9
Find
x2 + 6x = –12
Rewrite so all terms containing x are on one side.
x2 + 6x + 9 = –12 + 9
Complete the square by adding 9 to each side.
(x + 3)2 = –3
Factor the perfect square trinomial.
x + 3 = ± –3
Find the square root of each side.
x = –3 ± –3
Solve for x.
= –3 ± i –3
Simplify.

6. = Solve 2x2 + 7x – 1 = 0. x2 + x – = 0 Divide each side by 2. x2 + x =
Completing the Square
Lesson 5-7
Additional Examples
Solve 2x2 + 7x – 1 = 0.
x x – = 0 7 2 1
Divide each side by 2.
x x = 1 2 7
Rewrite so all terms containing x are on one side. = 7 2 49 16
Find b
x x = + 7 2 49 16 1
Complete the square by adding to each side.
x = 7 4 57 16
Factor the perfect square trinomial. 2 7 4 57
x + = ±
Find the square root of each side.
x = – ± 7 4
Solve for x. 57

7. Write y = x2 + 5x + 2 in vertex form.
Completing the Square
Lesson 5-7
Additional Examples
Write y = x2 + 5x + 2 in vertex form.
y = x2 + 5x + 2
= x2 + 5x – 5 2
Complete the square. Add and subtract
on the right side.
= x – 25 4 5 2
Factor the perfect square trinomial.
= x – 5 2 17 4
Simplify.
The vertex form is y = x – . 5 2 17 4

8. Factor –1 from the first two terms.
Completing the Square
Lesson 5-7
Additional Examples
The monthly profit P from the sales of rugs woven by a family rug-making business depends on the price r that they charge for a rug. The profit is model by P = –r r – 59,500. Write the function in vertex form. Use the vertex form to find the price that yields the maximum monthly profit and the amount of the maximum profit.
P = –r r – 59,500
= –(r 2 – 500r) – 59,500
Factor –1 from the first two terms.
= –[r 2 – 500r + (–250)2] – 59,500 + (–250)2
Add and subtract (–250)2 on the right side.
= –(r – 250)2 – 59, ,500
Factor the perfect square trinomial.
= –(r – 250)2 + 3,000
Simplify in vertex form.
The vertex is (250, 3,000). A price of $250 per rug gives a maximum monthly profit of $3,000.