Solve 112(1+a)^2=340.5

$$112 ( 1 + a ) ^ { 2 } = 340.5$$

Solve for a

$$a=\frac{\sqrt{9534}}{56}-1\approx 0.743610786$$

$$a=-\frac{\sqrt{9534}}{56}-1\approx -2.743610786$$

Steps by Finding Square Root

Divide both sides by 112.

$$\frac{112\left(a+1\right)^{2}}{112}=\frac{340.5}{112}$$

Dividing by 112 undoes the multiplication by 112.

$$\left(a+1\right)^{2}=\frac{340.5}{112}$$

Divide 340.5 by 112.

$$\left(a+1\right)^{2}=\frac{681}{224}$$

Take the square root of both sides of the equation.

$$a+1=\frac{\sqrt{9534}}{56} a+1=-\frac{\sqrt{9534}}{56}$$

Subtract 1 from both sides of the equation.

$$a+1-1=\frac{\sqrt{9534}}{56}-1 a+1-1=-\frac{\sqrt{9534}}{56}-1$$

Subtracting 1 from itself leaves 0.

$$a=\frac{\sqrt{9534}}{56}-1 a=-\frac{\sqrt{9534}}{56}-1$$