Since \(2\times 2=4\), the square root of \(4\) is \(2\).
\[2\sqrt{m}=\frac{{2}^{2}-5}{2}\]
Simplify \({2}^{2}\) to \(4\).
\[2\sqrt{m}=\frac{4-5}{2}\]
Simplify \(4-5\) to \(-1\).
\[2\sqrt{m}=\frac{-1}{2}\]
Move the negative sign to the left.
\[2\sqrt{m}=-\frac{1}{2}\]
Square both sides.
\[4m=\frac{1}{4}\]
Divide both sides by \(4\).
\[m=\frac{\frac{1}{4}}{4}\]
Simplify \(\frac{\frac{1}{4}}{4}\) to \(\frac{1}{4\times 4}\).
\[m=\frac{1}{4\times 4}\]
Simplify \(4\times 4\) to \(16\).
\[m=\frac{1}{16}\]
Check solution
When \(m=\frac{1}{16}\), the original equation \(\sqrt{4m}=\frac{{2}^{2}-5}{2}\) does not hold true.We will drop \(m=\frac{1}{16}\) from the solution set.
