Solve (10+x)sqrt{3}=x

$$( 10 + x ) \sqrt { 3 } = x$$

Solve for x

$$x=-5\sqrt{3}-15\approx -23.660254038$$

Steps for Solving Linear Equation

Use the distributive property to multiply 10+x by \sqrt{3}.

$$10\sqrt{3}+x\sqrt{3}=x$$

Subtract x from both sides.

$$10\sqrt{3}+x\sqrt{3}-x=0$$

Subtract 10\sqrt{3} from both sides. Anything subtracted from zero gives its negation.

$$x\sqrt{3}-x=-10\sqrt{3}$$

Combine all terms containing x.

$$\left(\sqrt{3}-1\right)x=-10\sqrt{3}$$

Divide both sides by \sqrt{3}-1.

$$\frac{\left(\sqrt{3}-1\right)x}{\sqrt{3}-1}=-\frac{10\sqrt{3}}{\sqrt{3}-1}$$

Dividing by \sqrt{3}-1 undoes the multiplication by \sqrt{3}-1.

$$x=-\frac{10\sqrt{3}}{\sqrt{3}-1}$$

Divide -10\sqrt{3} by \sqrt{3}-1.

$$x=-5\sqrt{3}-15$$