Solve for x
x=1
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\left(\sqrt{x+3}\right)^{2}=\left(\sqrt{5-x}\right)^{2}
Square both sides of the equation.
x+3=\left(\sqrt{5-x}\right)^{2}
Calculate \sqrt{x+3} to the power of 2 and get x+3.
x+3=5-x
Calculate \sqrt{5-x} to the power of 2 and get 5-x.
x+3+x=5
Add x to both sides.
2x+3=5
Combine x and x to get 2x.
2x=5-3
Subtract 3 from both sides.
2x=2
Subtract 3 from 5 to get 2.
x=\frac{2}{2}
Divide both sides by 2.
x=1
Divide 2 by 2 to get 1.
\sqrt{1+3}=\sqrt{5-1}
Substitute 1 for x in the equation \sqrt{x+3}=\sqrt{5-x}.
2=2
Simplify. The value x=1 satisfies the equation.
x=1
Equation \sqrt{x+3}=\sqrt{5-x} has a unique solution.
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