Solve 2x+xsqrt{3}=8sqrt{2}+x

$$2x+x \sqrt{ 3 } =8 \sqrt{ 2 } +x$$

Solve for x

$$x=4\sqrt{2}\left(\sqrt{3}-1\right)\approx 4.141104722$$

Steps for Solving Linear Equation

Subtract x from both sides.

$$2x+x\sqrt{3}-x=8\sqrt{2}$$

Combine 2x and -x to get x.

$$x+x\sqrt{3}=8\sqrt{2}$$

Combine all terms containing x.

$$\left(1+\sqrt{3}\right)x=8\sqrt{2}$$

The equation is in standard form.

$$\left(\sqrt{3}+1\right)x=8\sqrt{2}$$

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

$$\frac{\left(\sqrt{3}+1\right)x}{\sqrt{3}+1}=\frac{8\sqrt{2}}{\sqrt{3}+1}$$

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

$$x=\frac{8\sqrt{2}}{\sqrt{3}+1}$$

Divide 8\sqrt{2} by 1+\sqrt{3}.

$$x=4\sqrt{2}\left(\sqrt{3}-1\right)$$