Solve (2+2x)sqrt{2}=3+2x

$$(2+2x) \sqrt{ 2 } =3+2x$$

Solve for x

$$x=\frac{\sqrt{2}-1}{2}\approx 0.207106781$$

Steps for Solving Linear Equation

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

$$2\sqrt{2}+2x\sqrt{2}=3+2x$$

Subtract 2x from both sides.

$$2\sqrt{2}+2x\sqrt{2}-2x=3$$

Subtract 2\sqrt{2} from both sides.

$$2x\sqrt{2}-2x=3-2\sqrt{2}$$

Combine all terms containing x.

$$\left(2\sqrt{2}-2\right)x=3-2\sqrt{2}$$

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

$$\frac{\left(2\sqrt{2}-2\right)x}{2\sqrt{2}-2}=\frac{3-2\sqrt{2}}{2\sqrt{2}-2}$$

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

$$x=\frac{3-2\sqrt{2}}{2\sqrt{2}-2}$$

Divide 3-2\sqrt{2} by 2\sqrt{2}-2.

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