Solve sqrt{10}x+10x-5-2sqrt{5}=0

$$\sqrt { 10 } x + 10 x - 5 - 2 \sqrt { 5 } = 0$$

Solve for x

$$x=\frac{2\sqrt{5}}{9}-\frac{\sqrt{2}}{9}-\frac{\sqrt{10}}{18}+\frac{5}{9}\approx 0.719642618$$

Steps for Solving Linear Equation

Add 5 to both sides. Anything plus zero gives itself.

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

Add 2\sqrt{5} to both sides.

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

Combine all terms containing x.

$$\left(\sqrt{10}+10\right)x=5+2\sqrt{5}$$

The equation is in standard form.

$$\left(\sqrt{10}+10\right)x=2\sqrt{5}+5$$

Divide both sides by \sqrt{10}+10.

$$\frac{\left(\sqrt{10}+10\right)x}{\sqrt{10}+10}=\frac{2\sqrt{5}+5}{\sqrt{10}+10}$$

Dividing by \sqrt{10}+10 undoes the multiplication by \sqrt{10}+10.

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

Divide 5+2\sqrt{5} by \sqrt{10}+10.

$$x=\frac{\sqrt{2}\left(2\sqrt{10}+5\sqrt{2}-\sqrt{5}-2\right)}{18}$$