Solve sqrt{2}x+2(sqrt{2}+2)=sqrt{2}

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

Solve for x

$$x=-2\sqrt{2}-1\approx -3.828427125$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2 by \sqrt{2}+2.

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

Subtract 2\sqrt{2} from both sides.

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

Combine \sqrt{2} and -2\sqrt{2} to get -\sqrt{2}.

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

Subtract 4 from both sides.

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

Divide both sides by \sqrt{2}.

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

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

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

Divide -\sqrt{2}-4 by \sqrt{2}.

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