Answer
$x= 4, x= 8$
Work Step by Step
Use the square root method.
$$
\begin{aligned}
47 & =-4(6-x)^2+63 \\
47-63 & =-4(6-x)^2 \\
-16 & =-4(6-x)^2 \\
\frac{-16}{-4} & =(6-x)^2 \\
4 & =(6-x)^2 \\
\pm \sqrt{4} & =6-x \\
\pm 2 & =6-x.
\end{aligned}
$$ Find the two values of $x$ .
$$
\begin{aligned}
6-x & =2 \\
-x & =2-6 \\
-x & =-4 \\
x & =4
\end{aligned}
$$ $$
\begin{aligned}
6-x & =-2 \\
-x & =-2-6 \\
-x & =-8 \\
x & =8.
\end{aligned}
$$ Define the following version of the function and plot it. We see that the zeros are where they should be.
$$ f(x) = (6-x)^2-4$$
