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Mathematics
Problem
Patricia is trying to solve the following equation by completing the square:
25
x
2
+
20
x
−
10
=
0
25x^2 + 20x - 10 = 0
25
x
2
+
20
x
−
10
=
0
. She successfully rewrites the above equation in the following form:
(
a
x
+
b
)
2
=
c
(ax + b)^2 = c
(
a
x
+
b
)
2
=
c
, where
a
a
a
,
b
b
b
, and
c
c
c
are integers and
a
>
0
a > 0
a
>
0
. What is the value of
a
+
b
+
c
a + b + c
a
+
b
+
c
?
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