Solution: Solve the equation for real values of x - Art Of Mathematics

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Solve the equation

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This is how to solve this type of equation:

\[\begin{aligned} &\sqrt{x+15}+\sqrt{x}=15 \;\;\;\;\;\;\;\text { } (1) \\\\ &(\sqrt{x+15}+\sqrt{x})(\sqrt{x+15}-\sqrt{x})=15(\sqrt{x+15}-\sqrt{x}) \\\\ &x+15-x=15(\sqrt{x+15}-\sqrt{x}) \\\\ &15=15(\sqrt{x+15}-\sqrt{x}) \\\\ &(\sqrt{x+15}-\sqrt{x})=1 \;\;\;\;\;\;\;\text { } (2)\\\\ &\text { Using } (1) \text { and } (2) \\\\ &2 \sqrt{x+15}=16 \\\\ &\sqrt{x+15}=8 \\\\ &x+15=64 \\\\ &x=49 \end{aligned}\]

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