Solve (1/2a-3)^2=(1/2)

$$( \frac { 1 } { 2 } a - 3 ) ^ { 2 } = ( \frac { 1 } { 2 } )$$

Solve for a

$$a=\sqrt{2}+6\approx 7.414213562$$

$$a=6-\sqrt{2}\approx 4.585786438$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$\frac{1}{2}a-3=\frac{\sqrt{2}}{2} \frac{1}{2}a-3=-\frac{\sqrt{2}}{2}$$

Add 3 to both sides of the equation.

$$\frac{1}{2}a-3-\left(-3\right)=\frac{\sqrt{2}}{2}-\left(-3\right) \frac{1}{2}a-3-\left(-3\right)=-\frac{\sqrt{2}}{2}-\left(-3\right)$$

Subtracting -3 from itself leaves 0.

$$\frac{1}{2}a=\frac{\sqrt{2}}{2}-\left(-3\right) \frac{1}{2}a=-\frac{\sqrt{2}}{2}-\left(-3\right)$$

Subtract -3 from \frac{\sqrt{2}}{2}.

$$\frac{1}{2}a=\frac{\sqrt{2}}{2}+3$$

Subtract -3 from -\frac{\sqrt{2}}{2}.

$$\frac{1}{2}a=-\frac{\sqrt{2}}{2}+3$$

Multiply both sides by 2.

$$\frac{\frac{1}{2}a}{\frac{1}{2}}=\frac{\frac{\sqrt{2}}{2}+3}{\frac{1}{2}} \frac{\frac{1}{2}a}{\frac{1}{2}}=\frac{-\frac{\sqrt{2}}{2}+3}{\frac{1}{2}}$$

Dividing by \frac{1}{2} undoes the multiplication by \frac{1}{2}.

$$a=\frac{\frac{\sqrt{2}}{2}+3}{\frac{1}{2}} a=\frac{-\frac{\sqrt{2}}{2}+3}{\frac{1}{2}}$$

Divide \frac{\sqrt{2}}{2}+3 by \frac{1}{2} by multiplying \frac{\sqrt{2}}{2}+3 by the reciprocal of \frac{1}{2}.

$$a=\sqrt{2}+6$$

Divide -\frac{\sqrt{2}}{2}+3 by \frac{1}{2} by multiplying -\frac{\sqrt{2}}{2}+3 by the reciprocal of \frac{1}{2}.

$$a=6-\sqrt{2}$$

The equation is now solved.

$$a=\sqrt{2}+6 a=6-\sqrt{2}$$