Solve (a-3)^2=7

$$( a - 3 ) ^ { 2 } = 7$$

Solve for a

$$a=\sqrt{7}+3\approx 5.645751311$$

$$a=3-\sqrt{7}\approx 0.354248689$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$a-3=\sqrt{7} a-3=-\sqrt{7}$$

Add 3 to both sides of the equation.

$$a-3-\left(-3\right)=\sqrt{7}-\left(-3\right) a-3-\left(-3\right)=-\sqrt{7}-\left(-3\right)$$

Subtracting -3 from itself leaves 0.

$$a=\sqrt{7}-\left(-3\right) a=-\sqrt{7}-\left(-3\right)$$

Subtract -3 from \sqrt{7}.

$$a=\sqrt{7}+3$$

Subtract -3 from -\sqrt{7}.

$$a=3-\sqrt{7}$$

The equation is now solved.

$$a=\sqrt{7}+3 a=3-\sqrt{7}$$