Multiply both sides by \({(1-x)}^{2}\).
\[4{(1-x)}^{2}=9\]
Divide both sides by \(4\).
\[{(1-x)}^{2}=\frac{9}{4}\]
Take the square root of both sides.
\[1-x=\pm \sqrt{\frac{9}{4}}\]
Simplify \(\sqrt{\frac{9}{4}}\) to \(\frac{\sqrt{9}}{\sqrt{4}}\).
\[1-x=\pm \frac{\sqrt{9}}{\sqrt{4}}\]
Since \(3\times 3=9\), the square root of \(9\) is \(3\).
\[1-x=\pm \frac{3}{\sqrt{4}}\]
Since \(2\times 2=4\), the square root of \(4\) is \(2\).
\[1-x=\pm \frac{3}{2}\]
Break down the problem into these 2 equations.
\[1-x=\frac{3}{2}\]
\[1-x=-\frac{3}{2}\]
Solve the 1st equation: \(1-x=\frac{3}{2}\).
Subtract \(1\) from both sides.
\[-x=\frac{3}{2}-1\]
Simplify \(\frac{3}{2}-1\) to \(\frac{1}{2}\).
\[-x=\frac{1}{2}\]
Multiply both sides by \(-1\).
\[x=-\frac{1}{2}\]
\[x=-\frac{1}{2}\]
Solve the 2nd equation: \(1-x=-\frac{3}{2}\).
Subtract \(1\) from both sides.
\[-x=-\frac{3}{2}-1\]
Simplify \(-\frac{3}{2}-1\) to \(-\frac{5}{2}\).
\[-x=-\frac{5}{2}\]
Multiply both sides by \(-1\).
\[x=\frac{5}{2}\]
\[x=\frac{5}{2}\]
Collect all solutions.
\[x=-\frac{1}{2},\frac{5}{2}\]
Decimal Form: -0.5, 2.5
x=-1/2,5/2
