Solve x+5=xsqrt{2}

$$x + 5 = x \sqrt { 2 }$$

Solve for x

$$x=5\left(\sqrt{2}+1\right)\approx 12.071067812$$

Steps for Solving Linear Equation

Subtract x\sqrt{2} from both sides.

$$x+5-x\sqrt{2}=0$$

Subtract 5 from both sides. Anything subtracted from zero gives its negation.

$$x-x\sqrt{2}=-5$$

Combine all terms containing x.

$$\left(1-\sqrt{2}\right)x=-5$$

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

$$\frac{\left(1-\sqrt{2}\right)x}{1-\sqrt{2}}=-\frac{5}{1-\sqrt{2}}$$

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

$$x=-\frac{5}{1-\sqrt{2}}$$

Divide -5 by 1-\sqrt{2}.

$$x=5\sqrt{2}+5$$