Solve (a-8)^2-3=10

$$( a - 8 ) ^ { 2 } - 3 = 10$$

Solve for a

$$a=\sqrt{13}+8\approx 11.605551275$$

$$a=8-\sqrt{13}\approx 4.394448725$$

Steps by Finding Square Root

Add 3 to both sides of the equation.

$$\left(a-8\right)^{2}-3+3=10+3$$

Subtracting 3 from itself leaves 0.

$$\left(a-8\right)^{2}=10+3$$

Add 10 to 3.

$$\left(a-8\right)^{2}=13$$

Take the square root of both sides of the equation.

$$a-8=\sqrt{13} a-8=-\sqrt{13}$$

Add 8 to both sides of the equation.

$$a-8-\left(-8\right)=\sqrt{13}-\left(-8\right) a-8-\left(-8\right)=-\sqrt{13}-\left(-8\right)$$

Subtracting -8 from itself leaves 0.

$$a=\sqrt{13}-\left(-8\right) a=-\sqrt{13}-\left(-8\right)$$

Subtract -8 from \sqrt{13}.

$$a=\sqrt{13}+8$$

Subtract -8 from -\sqrt{13}.

$$a=8-\sqrt{13}$$

The equation is now solved.

$$a=\sqrt{13}+8 a=8-\sqrt{13}$$