Solve (a-7)^2+5=55

$$( a - 7 ) ^ { 2 } + 5 = 55$$

Solve for a

$$a=5\sqrt{2}+7\approx 14.071067812$$

$$a=7-5\sqrt{2}\approx -0.071067812$$

Steps by Finding Square Root

Subtract 5 from both sides of the equation.

$$\left(a-7\right)^{2}+5-5=55-5$$

Subtracting 5 from itself leaves 0.

$$\left(a-7\right)^{2}=55-5$$

Subtract 5 from 55.

$$\left(a-7\right)^{2}=50$$

Take the square root of both sides of the equation.

$$a-7=5\sqrt{2} a-7=-5\sqrt{2}$$

Add 7 to both sides of the equation.

$$a-7-\left(-7\right)=5\sqrt{2}-\left(-7\right) a-7-\left(-7\right)=-5\sqrt{2}-\left(-7\right)$$

Subtracting -7 from itself leaves 0.

$$a=5\sqrt{2}-\left(-7\right) a=-5\sqrt{2}-\left(-7\right)$$

Subtract -7 from 5\sqrt{2}.

$$a=5\sqrt{2}+7$$

Subtract -7 from -5\sqrt{2}.

$$a=7-5\sqrt{2}$$

The equation is now solved.

$$a=5\sqrt{2}+7 a=7-5\sqrt{2}$$