Name
Date
Class
Reteach
LESSON
5-4
Completing the Square
You can use the square root property to solve some quadratic equations.
Square Root Property
2
To solve x a,
take the square root
of both sides of the
equation.
x2 a
Remember:
a
x 2 2
2
2 4, and 2 4.
x a
2
Solve 4x 5 43.
2
4x 48
The coefficient of x 2 should
be 1 to use the square root
property.
Add 5 to both sides.
2
x 12
Divide both sides by 4.
2
x 12
Take the square root of both sides.
x 12
Simplify.
Think: 12 4 3 4 3 2 3
x 23
2
Solve x 12x 36 50.
x 6 2 50
Factor the perfect square trinomial.
2
x 6 50 Take the square root of both sides.
x 6 50
Subtract 6 from both sides.
x 6 50
Simplify.
Think: 50 25 2 25 2 5 2
x 6 52
Solve each equation.
1. 3x 7 31
2. x 8x 16 18
2
3x 2 2
2
x 4 18
24
x2 8
x 4 18
x 2 2
x 4 3 2
3. 6x 2 4 38
4. x 2 2x 1 10
6x 2 42
x2 7
x
x 1 10
x 7
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
a207c05-4_rt.indd 30
1 2 10
x 1 10
30
Holt Algebra 2
12/15/05 4:35:21 PM
Process Black
Name
Date
Class
Reteach
LESSON
5-4
Completing the Square (continued)
You can use a process called completing the square to rewrite
a quadratic of the form x 2 bx as a perfect square trinomial.
To complete the
square of x 2 bx,
b 2.
add __
2
Think: Multiply the
coefficient of x by
1 . Then square it.
__
2
x __2b 2
b
x bx __
2
2
2
Complete the square: x 2 8x ?.
Identify b, the coefficient of x : b 8.
Step 1
Step 2
Step 3
Step 4
8
__b2 ___
2 b 2:
Find __
2
b 2:
Add __
2
2
x 2 8x 16
Factor:
x 2 8x 16 x 4 2
2
4 2 16
Check: x 4 2 x 4 x 4 b as a factor.
Use __
2
x 2 8x 16 ✓
Complete each square and factor.
2
5. x 9x ?
6. x 2 4x ?
9
b __
b 9, so __
2
2
2 b
__
2
81
___
4
b
4 , so __b 2
__b2 2
2
4
81
___
4
x 9x 2
x 9
__
2
4
x 4x 2
2
x
7. x 2 10x ?
8. x 2 3x ?
9
x 2 3x __
4
x 2 10x 25
x
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
a207c05-4_rt.indd 31
2 2
5 2
31
3
x __
2
2
Holt Algebra 2
12/15/05 4:35:22 PM
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