Name
Date
Class
Reteach
LESSON
9-7
Solving Quadratic Equations by Using Square Roots
If a quadratic equation is in the form x 2 a, you must take the square root of both sides to
find the solutions. Remember to find both the positive and negative square roots.
Solve x 2 ⫽ 36 using square roots.
Check:
2
x 36
2
x 36
Take the square root of
both sides.
x 6
x⫽6
x ⫽ ⫺6
2
x 36
x 2 36
?
6 2 36
?
6 2 36
?
The solutions are 6 and 6.
36 36✓
Solve 2x 2 ⫹ 7 ⫽ 207 using square roots.
Check:
2
2x 7 207
x ⫽ 10
7
7
x ⫽ ⫺10
?
?
2
2x 7 207
Add 7 to both sides.
?
2x 2 7 207
2
2 10 7 207
2
2x 200
200
2___
x 2 ____
2
2
?
36 36✓
?
2 10 2 7 207
?
?
2 100 7 207 2 100 7 207
Divide both sides
by 2.
?
200 7 207
?
x 2 100 Take the square root of
207 207✓
?
200 7 207
?
207 207✓
both sides.
x 10
The solutions are 10 and 10.
Solve using square roots.
1. x 2 81
2. x 2 9
⫾9
3. x 2 64
⫾3
4. x 2 44 188
5. x 2 12 37
⫾12
⫾7
7. 3x 2 25 73
8. 5x 2 9 116
⫾4
⫾5
10. 4x 2 11 25
11. x 2 13 87
⫾3
⫾10
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
a107c09-7_rt.indd 54
54
no solution
6. x 2 10 131
⫾11
9. 4x 2 42 102
⫾6
12. 3x 2 200 8
⫾8
Holt Algebra 1
12/26/05 8:42:30 AM
Process Black
Name
Date
Class
Reteach
LESSON
9-7
Solving Quadratic Equations by Using Square Roots (continued)
Remember, the square root of a number is not always a perfect square. You can use a
calculator to approximate the answer.
Solve x 2 ⫹ 6 ⫽ 24. Round to the nearest hundredth.
2
x 6 24
6 6
Add 6 to both sides
2
x 18
x 2 18
Take the square root of both sides.
x 18
2
x 4.24
Evaluate 18 on a calculator.
The approximate solutions are 4.24 and 4.24.
When solving application problems by using square roots, one of the solutions
may not make sense.
The length of a rectangle is 5 times the width. The area of the rectangle is
210 square feet. Find the width. Round to the nearest tenth of a foot.
5w w 210
lw A
W
5w 210
2
210
5____
w ____
5
5
w 2 42
2
W
2
w 42
w 6.5
It does not make sense for the width to be a negative number.
Therefore, the only solution is 6.5 feet.
Solve. Round to the nearest hundredth.
2
13. x 50
14. x 2 8 20
⫾7.07
15. 2x 2 21 81
⫾3.46
⫾5.48
16. A triangle has a base that is 3 times the height. The area of the
2
triangle is 63 cm . Find the height of the triangle. Round your
1bh .
answer to the nearest tenth of a centimeter. A __
2
17. The length of a rectangle is 4 times the width. The area of the
rectangle is 850 square inches. Find the width. Round to
the nearest tenth of an inch.
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
a107c09-7_rt.indd 55
55
6.48 cm
14.6 in
Holt Algebra 1
12/26/05 8:42:31 AM
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Holt Algebra 1
12/29/05 2:16:48 PM