Solve (1/2x)4=1/2(2sqrt{2}a+y)*2sqrt{2}

$$( \frac { 1 } { 2 } x ) 4 = \frac { 1 } { 2 } ( 2 \sqrt { 2 } a + y ) \cdot 2 \sqrt { 2 }$$

Solve for a

$$a=-\frac{\sqrt{2}y}{4}+\frac{x}{2}$$

Steps for Solving Linear Equation

Cancel out \frac{1}{2} on both sides.

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

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

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

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

$$x\times 4=4a\left(\sqrt{2}\right)^{2}+2y\sqrt{2}$$

The square of \sqrt{2} is 2.

$$x\times 4=4a\times 2+2y\sqrt{2}$$

Multiply 4 and 2 to get 8.

$$x\times 4=8a+2y\sqrt{2}$$

Swap sides so that all variable terms are on the left hand side.

$$8a+2y\sqrt{2}=x\times 4$$

Subtract 2y\sqrt{2} from both sides.

$$8a=x\times 4-2y\sqrt{2}$$

The equation is in standard form.

$$8a=-2\sqrt{2}y+4x$$

Divide both sides by 8.

$$\frac{8a}{8}=\frac{-2\sqrt{2}y+4x}{8}$$

Dividing by 8 undoes the multiplication by 8.

$$a=\frac{-2\sqrt{2}y+4x}{8}$$

Divide 4x-2\sqrt{2}y by 8.

$$a=-\frac{\sqrt{2}y}{4}+\frac{x}{2}$$

Solve for x

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

Steps for Solving Linear Equation

Cancel out \frac{1}{2} on both sides.

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

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

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

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

$$x\times 4=4a\left(\sqrt{2}\right)^{2}+2y\sqrt{2}$$

The square of \sqrt{2} is 2.

$$x\times 4=4a\times 2+2y\sqrt{2}$$

Multiply 4 and 2 to get 8.

$$x\times 4=8a+2y\sqrt{2}$$

The equation is in standard form.

$$4x=2\sqrt{2}y+8a$$

Divide both sides by 4.

$$\frac{4x}{4}=\frac{2\sqrt{2}y+8a}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$x=\frac{2\sqrt{2}y+8a}{4}$$

Divide 8a+2y\sqrt{2} by 4.

$$x=\frac{\sqrt{2}y}{2}+2a$$