Solve 2(x-sqrt{5})=sqrt{500}

$$2 ( x - \sqrt { 5 } ) = \sqrt { 500 }$$

Solve for x

$$x=6\sqrt{5}\approx 13.416407865$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2 by x-\sqrt{5}.

$$2x-2\sqrt{5}=\sqrt{500}$$

Factor 500=10^{2}\times 5. Rewrite the square root of the product \sqrt{10^{2}\times 5} as the product of square roots \sqrt{10^{2}}\sqrt{5}. Take the square root of 10^{2}.

$$2x-2\sqrt{5}=10\sqrt{5}$$

Add 2\sqrt{5} to both sides.

$$2x=10\sqrt{5}+2\sqrt{5}$$

Combine 10\sqrt{5} and 2\sqrt{5} to get 12\sqrt{5}.

$$2x=12\sqrt{5}$$

Divide both sides by 2.

$$\frac{2x}{2}=\frac{12\sqrt{5}}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$x=\frac{12\sqrt{5}}{2}$$

Divide 12\sqrt{5} by 2.

$$x=6\sqrt{5}$$