Let
f
(
x
)
=
x
2
\displaystyle {f{{\left({x}\right)}}}={x}^{{2}}
f
(
x
)
=
x
2
and
g
(
x
)
=
(
x
−
5
)
2
+
30.
\displaystyle {g{{\left({x}\right)}}}={\left({x}-{5}\right)}^{{2}}+{30}.
g
(
x
)
=
(
x
−
5
)
2
+
30
.
There is one line with positive slope that is tangent to both of the parabolas
y
=
f
(
x
)
\displaystyle {y}={f{{\left({x}\right)}}}
y
=
f
(
x
)
and
y
=
g
(
x
)
\displaystyle {y}={g{{\left({x}\right)}}}
y
=
g
(
x
)
simultaneously.
Find the equation of the line.
y=
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