Solve x=frac{(5-sqrt{5})sqrt{10+25}}{20}

$$x = \frac { ( 5 - \sqrt { 5 } ) \sqrt { 10 + 25 } } { 20 }$$

Solve for x

$$x=\frac{\sqrt{35}-\sqrt{7}}{4}\approx 0.817582118$$

Steps for Solving Linear Equation

Add 10 and 25 to get 35.

$$x=\frac{\left(5-\sqrt{5}\right)\sqrt{35}}{20}$$

Use the distributive property to multiply 5-\sqrt{5} by \sqrt{35}.

$$x=\frac{5\sqrt{35}-\sqrt{5}\sqrt{35}}{20}$$

Factor 35=5\times 7. Rewrite the square root of the product \sqrt{5\times 7} as the product of square roots \sqrt{5}\sqrt{7}.

$$x=\frac{5\sqrt{35}-\sqrt{5}\sqrt{5}\sqrt{7}}{20}$$

Multiply \sqrt{5} and \sqrt{5} to get 5.

$$x=\frac{5\sqrt{35}-5\sqrt{7}}{20}$$

Divide each term of 5\sqrt{35}-5\sqrt{7} by 20 to get \frac{1}{4}\sqrt{35}-\frac{1}{4}\sqrt{7}.

$$x=\frac{1}{4}\sqrt{35}-\frac{1}{4}\sqrt{7}$$

Assign x

$$x≔\frac{\sqrt{7}\left(\sqrt{5}-1\right)}{4}$$