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3 votes
HELP PLEASE!!!

Sonia graphs the equation y=-x^2+4x and y=x-4 to solve the equation -x^2+4x=x-4. Her graph is shown below.
what are the solutions of -x^2+4x=x-4?
a)-5 and 0
b)-5 and -1
c)-1 and 4
d)0 and 4

HELP PLEASE!!! Sonia graphs the equation y=-x^2+4x and y=x-4 to solve the equation-example-1

1 Answer

6 votes


x
2
+
4
x
=
x

4
-
x
2
+
4
x
=
x
-
4
Move all terms to the left side of the equation and simplify.
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x
2
+
3
x
+
4
=
0
-
x
2
+
3
x
+
4
=
0
Use the quadratic formula to find the solutions.

b
±

b
2

4
(
a
c
)
2
a
-
b
±
b
2
-
4
(
a
c
)
2
a
Substitute the values
a
=

1
a
=
-
1
,
b
=
3
b
=
3
, and
c
=
4
c
=
4
into the quadratic formula and solve for
x
x
.

3
±

3
2

4

(

1

4
)
2


1
-
3
±
3
2
-
4

(
-
1

4
)
2

-
1
Simplify.
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x
=
3
±
5
2
x
=
3
±
5
2
The final answer is the combination of both solutions.
x
=
4
,

1
User Zomega
by
8.3k points