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Let’s check out your problem:
(
x
+
3
)
2
−
49
=
0
(x+3)^{2}-49=0
(
x
+
3
)
2
−
49
=
0
\newline
What are the solutions to the given equation?
\newline
Choose
1
1
1
answer:
\newline
(A)
x
=
−
4
,
x
=
−
10
x=-4, x=-10
x
=
−
4
,
x
=
−
10
\newline
(B)
x
=
4
,
x
=
−
10
x=4, x=-10
x
=
4
,
x
=
−
10
\newline
(C)
x
=
4
,
x
=
10
x=4, x=10
x
=
4
,
x
=
10
\newline
(D)
x
=
−
4
,
x
=
10
x=-4, x=10
x
=
−
4
,
x
=
10
View step-by-step help
Home
Math Problems
Algebra 1
Solve linear equations: mixed review
Full solution
Q.
(
x
+
3
)
2
−
49
=
0
(x+3)^{2}-49=0
(
x
+
3
)
2
−
49
=
0
\newline
What are the solutions to the given equation?
\newline
Choose
1
1
1
answer:
\newline
(A)
x
=
−
4
,
x
=
−
10
x=-4, x=-10
x
=
−
4
,
x
=
−
10
\newline
(B)
x
=
4
,
x
=
−
10
x=4, x=-10
x
=
4
,
x
=
−
10
\newline
(C)
x
=
4
,
x
=
10
x=4, x=10
x
=
4
,
x
=
10
\newline
(D)
x
=
−
4
,
x
=
10
x=-4, x=10
x
=
−
4
,
x
=
10
Simplify the factors:
Next, we simplify the
factors
:
\newline
(
x
+
10
)
(
x
−
4
)
=
0
(x+10)(x-4) = 0
(
x
+
10
)
(
x
−
4
)
=
0
\newline
This gives us two separate equations to solve for
x
x
x
:
\newline
x
+
10
=
0
x+10 = 0
x
+
10
=
0
or
x
−
4
=
0
x-4 = 0
x
−
4
=
0
Solve the first equation:
Now we solve each equation for
x
x
x
:
For the first equation:
x
+
10
=
0
x+10 = 0
x
+
10
=
0
x
=
−
10
x = -10
x
=
−
10
For the second equation:
x
−
4
=
0
x-4 = 0
x
−
4
=
0
x
=
4
x = 4
x
=
4
Solve the second equation:
We have found the two solutions to the equation:
\newline
x
=
−
10
x = -10
x
=
−
10
and
x
=
4
x = 4
x
=
4
\newline
These correspond to answer choice (B)
x
=
4
x=4
x
=
4
,
x
=
−
10
x=-10
x
=
−
10
.
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Solve for x.
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\newline
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How many solutions does the following equation have?
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y
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7
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Choose
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1
answer:
\newline
(A) No solutions
\newline
(B) Exactly one solution
\newline
(C) Infinitely many solutions
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How many solutions does the following equation have?
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9
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(
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\newline
Choose
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1
1
answer:
\newline
(A) No solutions
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(B) Exactly one solution
\newline
(C) Infinitely many solutions
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How many solutions does the following equation have?
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6
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x
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4
x
−
2
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−
6
(
x
+
7
)
=
−
4
x
−
2
\newline
Choose
1
1
1
answer:
\newline
(A) No solutions
\newline
(B) Exactly one solution
\newline
(C) Infinitely many solutions
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How many solutions does the following equation have?
\newline
−
4
x
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+
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=
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7
+
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10
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7
+
6
x
\newline
Choose
1
1
1
answer:
\newline
(A) No solutions
\newline
(B) Exactly one solution
\newline
(C) Infinitely many solutions
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How many solutions does the following equation have?
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17
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−
17
(
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−
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)
=
−
17
y
+
64
\newline
Choose
1
1
1
answer:
\newline
(A) No solutions
\newline
(B) Exactly one solution
\newline
(C) Infinitely many solutions
Get tutor help
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Question
How many solutions does the following equation have?
\newline
9
z
−
6
+
7
z
=
16
z
−
6
9z-6+7z=16z-6
9
z
−
6
+
7
z
=
16
z
−
6
\newline
Choose
1
1
1
answer:
\newline
(A) No solutions
\newline
(B) Exactly one solution
\newline
(C) Infinitely many solutions
Get tutor help
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