Basic Algebra Issue

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I have the equation $y+1 = \frac14x^2$. I tried to solve for $x$ (as seen in the picture). Please explain why only the right method is correct, and the left is wrong.

Thanks!

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It should be $\sqrt{y+1}=\color{red}{\frac12}x$. When taking square roots the constants must be rooted as well.