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Solve for x: sqrt(13-x)=sqrt(x-9)

Solve for x: $\sqrt{13-x} = \sqrt{x-9}$

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Multiply radical expressions

Full solution

Q. Solve for x:

\sqrt{13-x} = \sqrt{x-9}

Square Both Sides: Square both sides to eliminate the square roots, $\sqrt{13-x}^2 = \sqrt{x-9}^2$
Add $x$ to Isolate: Add $x$ to both sides to start isolating $x$ , $13 - x + x = x - 9 + x$
Add $9$ to Further Isolate: Add $9$ to both sides to further isolate $x$ , $13 + 9 = 2x - 9 + 9$
Divide to Solve for x: Divide both sides by $2$ to solve for $x$ , $22 / 2 = 2x / 2$
Check Solution: Check the solution by substituting $x$ back into the original equation, $\sqrt{13-11} = \sqrt{11-9}$

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