Solve 3sqrt{6}+2sqrt{2}=xsqrt{2}

$$3 \sqrt{ 6 } +2 \sqrt{ 2 } =x \sqrt{ 2 }$$

Solve for x

$$x=3\sqrt{3}+2\approx 7.196152423$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$x\sqrt{2}=3\sqrt{6}+2\sqrt{2}$$

The equation is in standard form.

$$\sqrt{2}x=2\sqrt{2}+3\sqrt{6}$$

Divide both sides by \sqrt{2}.

$$\frac{\sqrt{2}x}{\sqrt{2}}=\frac{2\sqrt{2}+3\sqrt{6}}{\sqrt{2}}$$

Dividing by \sqrt{2} undoes the multiplication by \sqrt{2}.

$$x=\frac{2\sqrt{2}+3\sqrt{6}}{\sqrt{2}}$$

Divide 3\sqrt{6}+2\sqrt{2} by \sqrt{2}.

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