Solve for x
x\in \begin{bmatrix}-\frac{\sqrt{5}}{5},\frac{\sqrt{5}}{5}\end{bmatrix}
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x^{2}\leq \frac{1}{5}
Divide both sides by 5. Since 5 is positive, the inequality direction remains the same.
x^{2}\leq \left(\frac{\sqrt{5}}{5}\right)^{2}
Calculate the square root of \frac{1}{5} and get \frac{\sqrt{5}}{5}. Rewrite \frac{1}{5} as \left(\frac{\sqrt{5}}{5}\right)^{2}.
|x|\leq \frac{\sqrt{5}}{5}
Inequality holds for |x|\leq \frac{\sqrt{5}}{5}.
x\in \begin{bmatrix}-\frac{\sqrt{5}}{5},\frac{\sqrt{5}}{5}\end{bmatrix}
Rewrite |x|\leq \frac{\sqrt{5}}{5} as x\in \left[-\frac{\sqrt{5}}{5},\frac{\sqrt{5}}{5}\right].
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