Section 9.3
S
olving Quadra
tic Equations
UsingSquare Roo
ts
501
Exerci
ses
9.3
Dynamic Solutions
available at
BigIdeasMath.c
om
In Exercises 3
–8
,
determine the number of real
solutionsof the equation. T
hen solve the equation using
square ro
ots.
3.
x
2
25
4.
x
2
36
5.
x
2
21
6.
x
2
400
7.
x
2
0
8.
x
2
169
In Exercises 9–
18,
solve the equation using square
roots.
(See Example 1.)
9.
x
2
16
0
10.
x
2
+
6
0
11.
3
x
2
+
12
0
12.
x
2
55
26
13.
2
x
2
98
0
14.
x
2
+
9
9
15.
3
x
2
5
5
16.
4
x
2
371
29
17.
4
x
2
+
10
11
18.
9
x
2
35
14
In Exercises 19
–2
4, solve the equation using square
roots.
(
See Example 2.)
19.
(
x
+
3)
2
0
20.
(
x
1)
2
4
21.
(2
x
1)
2
81
22.
(4
x
+
5)
2
9
23.
9(
x
+
1)
2
16
24.
4(
x
2)
2
25
In Exercises 25
–30
, solve the equation using square
roots. Round y
our solutio
ns to the nearest hundr
edth.
(See Example 3.)
25.
x
2
+
6
13
26.
x
2
+
11
24
27
.
2
x
2
9
11
28.
5
x
2
+
2
6
29.
21
15
2
x
2
30.
2
4
x
2
5
31.
ERROR ANAL
Y
SIS
Describe and correct the error in
solving the equation 2
x
2
33
39 using square roots.
2
x
2
−
33
=
39
2
x
2
=
72
x
2
=
36
x
=
6
The solu
tion is
x
=
6.
✗
32.
MODELING WITH
MA
THEMA
TICS
An in-ground
pondhas the shape of a rectangular prism. The
pond has a depth of 24 inches and a volume of
72,000 cubic inches. The length of the pond is
two times its width. Find the length and width of
the pond.
(
See Example 4.)
33.
MODELING WITH
MA
THEMA
TICS
A person sitting
in the top row
of the bleachers at a sporting ev
ent
drops a pair of sunglasses from a height of 24 feet.
The function
h
16
x
2
+
24 represents the height
h
(in feet) of the sunglasses after
x
seconds. How
long
does it take the sunglasses to hit the ground?
Monitoring P
rogres
s and Modeling
with Mathematic
s
Monitoring Progr
ess and
Modeling with Mathematics
1.
COMPLETE THE S
ENTENCE
The equation
x
2
d
has ____ real solutions when
d
>
0.
2.
DIFFERENT
WORDS
,
SAME QUESTION
Which is diff
erent? Find “both” answers.
Solve
x
2
144 using square roots.
Solve
x
2
144
0 using square roots.
Solve
x
2
+
146
2 using square roots.
Solve
x
2
+
2
146 using square roots.
Voca
bulary
and Core
Concept Check
Voca
bulary
and Core Concept
Check
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