Solve (1-x)sqrt{2}=x

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

Solve for x

$$x=2-\sqrt{2}\approx 0.585786438$$

Steps for Solving Linear Equation

Use the distributive property to multiply 1-x by \sqrt{2}.

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

Subtract x from both sides.

$$\sqrt{2}-x\sqrt{2}-x=0$$

Subtract \sqrt{2} from both sides. Anything subtracted from zero gives its negation.

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

Combine all terms containing x.

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

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

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

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

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

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

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