Solve xsqrt{2}-2sqrt{2}=x+2

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

Solve for x

$$x=4\sqrt{2}+6\approx 11.656854249$$

Steps for Solving Linear Equation

Subtract x from both sides.

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

Add 2\sqrt{2} to both sides.

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

Combine all terms containing x.

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

The equation is in standard form.

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

Divide both sides by \sqrt{2}-1.

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

Dividing by \sqrt{2}-1 undoes the multiplication by \sqrt{2}-1.

$$x=\frac{2\sqrt{2}+2}{\sqrt{2}-1}$$

Divide 2+2\sqrt{2} by \sqrt{2}-1.

$$x=4\sqrt{2}+6$$