Regroup terms.
\[{(4-x)}^{2}=256\]
Take the square root of both sides.
\[4-x=\pm \sqrt{256}\]
Since \(16\times 16=256\), the square root of \(256\) is \(16\).
\[4-x=\pm 16\]
Break down the problem into these 2 equations.
\[4-x=16\]
\[4-x=-16\]
Solve the 1st equation: \(4-x=16\).
Subtract \(4\) from both sides.
\[-x=16-4\]
Simplify \(16-4\) to \(12\).
\[-x=12\]
Multiply both sides by \(-1\).
\[x=-12\]
\[x=-12\]
Solve the 2nd equation: \(4-x=-16\).
Subtract \(4\) from both sides.
\[-x=-16-4\]
Simplify \(-16-4\) to \(-20\).
\[-x=-20\]
Multiply both sides by \(-1\).
\[x=20\]
\[x=20\]
Collect all solutions.
\[x=-12,20\]
x=-12,20
