Solve 4+x=2+sqrt{2}x

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

Solve for x

$$x=2\sqrt{2}+2\approx 4.828427125$$

Steps for Solving Linear Equation

Subtract \sqrt{2}x from both sides.

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

Subtract 4 from both sides.

$$x-\sqrt{2}x=2-4$$

Subtract 4 from 2 to get -2.

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

Combine all terms containing x.

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

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

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

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

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

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

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