Solve for x
x=9
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\left(\sqrt{x+5}\right)^{2}=\left(\sqrt{2x-4}\right)^{2}
Square both sides of the equation.
x+5=\left(\sqrt{2x-4}\right)^{2}
Calculate \sqrt{x+5} to the power of 2 and get x+5.
x+5=2x-4
Calculate \sqrt{2x-4} to the power of 2 and get 2x-4.
x+5-2x=-4
Subtract 2x from both sides.
-x+5=-4
Combine x and -2x to get -x.
-x=-4-5
Subtract 5 from both sides.
-x=-9
Subtract 5 from -4 to get -9.
x=9
Multiply both sides by -1.
\sqrt{9+5}=\sqrt{2\times 9-4}
Substitute 9 for x in the equation \sqrt{x+5}=\sqrt{2x-4}.
14^{\frac{1}{2}}=14^{\frac{1}{2}}
Simplify. The value x=9 satisfies the equation.
x=9
Equation \sqrt{x+5}=\sqrt{2x-4} has a unique solution.
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