Solve for x
x=\frac{\sqrt{5}x_{5}}{10}
Solve for x_5
x_{5}=2\sqrt{5}x
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x\times 2\sqrt{5}=x_{5}
Factor 20=2^{2}\times 5. Rewrite the square root of the product \sqrt{2^{2}\times 5} as the product of square roots \sqrt{2^{2}}\sqrt{5}. Take the square root of 2^{2}.
2\sqrt{5}x=x_{5}
The equation is in standard form.
\frac{2\sqrt{5}x}{2\sqrt{5}}=\frac{x_{5}}{2\sqrt{5}}
Divide both sides by 2\sqrt{5}.
x=\frac{x_{5}}{2\sqrt{5}}
Dividing by 2\sqrt{5} undoes the multiplication by 2\sqrt{5}.
x=\frac{\sqrt{5}x_{5}}{10}
Divide x_{5} by 2\sqrt{5}.
x\times 2\sqrt{5}=x_{5}
Factor 20=2^{2}\times 5. Rewrite the square root of the product \sqrt{2^{2}\times 5} as the product of square roots \sqrt{2^{2}}\sqrt{5}. Take the square root of 2^{2}.
x_{5}=x\times 2\sqrt{5}
Swap sides so that all variable terms are on the left hand side.
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