Solve sqrt{2}a+2a=4(sqrt{2}+1)

$$\sqrt { 2 } a + 2 a = 4 ( \sqrt { 2 } + 1 )$$

Solve for a

$$a=2\sqrt{2}\approx 2.828427125$$

Steps for Solving Linear Equation

Use the distributive property to multiply 4 by \sqrt{2}+1.

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

Combine all terms containing a.

$$\left(\sqrt{2}+2\right)a=4\sqrt{2}+4$$

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

$$\frac{\left(\sqrt{2}+2\right)a}{\sqrt{2}+2}=\frac{4\sqrt{2}+4}{\sqrt{2}+2}$$

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

$$a=\frac{4\sqrt{2}+4}{\sqrt{2}+2}$$

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

$$a=2\sqrt{2}$$