Solve 24+x=18sqrt{2}+sqrt{2}x

$$24+x=18 \sqrt{ 2 } + \sqrt{ 2 } x$$

Solve for x

$$x=6\left(\sqrt{2}-2\right)\approx -3.514718626$$

Steps for Solving Linear Equation

Subtract \sqrt{2}x from both sides.

$$24+x-\sqrt{2}x=18\sqrt{2}$$

Subtract 24 from both sides.

$$x-\sqrt{2}x=18\sqrt{2}-24$$

Combine all terms containing x.

$$\left(1-\sqrt{2}\right)x=18\sqrt{2}-24$$

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

$$\frac{\left(1-\sqrt{2}\right)x}{1-\sqrt{2}}=\frac{18\sqrt{2}-24}{1-\sqrt{2}}$$

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

$$x=\frac{18\sqrt{2}-24}{1-\sqrt{2}}$$

Divide 18\sqrt{2}-24 by 1-\sqrt{2}.

$$x=6\sqrt{2}-12$$