Solve 1.0*10^-6/d^2=5.25*10^-7/(3.4-2)^2

$$\frac { 1.0 \times 10 ^ { - 6 } } { d ^ { 2 } } = \frac { 5.25 \times 10 ^ { - 7 } } { ( 3.4 - 2 ) ^ { 2 } }$$

Solve for d

$$d = \frac{2 \sqrt{210}}{15} \approx 1.932183566$$

$$d = -\frac{2 \sqrt{210}}{15} \approx -1.932183566$$

Steps by Finding Square Root

Variable d cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by d^{2}.

$$1\times 10^{-6}=\frac{25}{49}d^{2}\times 5.25\times 10^{-7}$$

Calculate 10 to the power of -6 and get \frac{1}{1000000}.

$$1\times \frac{1}{1000000}=\frac{25}{49}d^{2}\times 5.25\times 10^{-7}$$

Multiply 1 and \frac{1}{1000000} to get \frac{1}{1000000}.

$$\frac{1}{1000000}=\frac{25}{49}d^{2}\times 5.25\times 10^{-7}$$

Multiply \frac{25}{49} and 5.25 to get \frac{75}{28}.

$$\frac{1}{1000000}=\frac{75}{28}d^{2}\times 10^{-7}$$

Calculate 10 to the power of -7 and get \frac{1}{10000000}.

$$\frac{1}{1000000}=\frac{75}{28}d^{2}\times \frac{1}{10000000}$$

Multiply \frac{75}{28} and \frac{1}{10000000} to get \frac{3}{11200000}.

$$\frac{1}{1000000}=\frac{3}{11200000}d^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{3}{11200000}d^{2}=\frac{1}{1000000}$$

Multiply both sides by \frac{11200000}{3}, the reciprocal of \frac{3}{11200000}.

$$d^{2}=\frac{1}{1000000}\times \frac{11200000}{3}$$

Multiply \frac{1}{1000000} and \frac{11200000}{3} to get \frac{56}{15}.

$$d^{2}=\frac{56}{15}$$

Take the square root of both sides of the equation.

$$d=\frac{2\sqrt{210}}{15} d=-\frac{2\sqrt{210}}{15}$$

Steps Using the Quadratic Formula

Variable d cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by d^{2}.

$$1\times 10^{-6}=\frac{25}{49}d^{2}\times 5.25\times 10^{-7}$$

Calculate 10 to the power of -6 and get \frac{1}{1000000}.

$$1\times \frac{1}{1000000}=\frac{25}{49}d^{2}\times 5.25\times 10^{-7}$$

Multiply 1 and \frac{1}{1000000} to get \frac{1}{1000000}.

$$\frac{1}{1000000}=\frac{25}{49}d^{2}\times 5.25\times 10^{-7}$$

Multiply \frac{25}{49} and 5.25 to get \frac{75}{28}.

$$\frac{1}{1000000}=\frac{75}{28}d^{2}\times 10^{-7}$$

Calculate 10 to the power of -7 and get \frac{1}{10000000}.

$$\frac{1}{1000000}=\frac{75}{28}d^{2}\times \frac{1}{10000000}$$

Multiply \frac{75}{28} and \frac{1}{10000000} to get \frac{3}{11200000}.

$$\frac{1}{1000000}=\frac{3}{11200000}d^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{3}{11200000}d^{2}=\frac{1}{1000000}$$

Subtract \frac{1}{1000000} from both sides.

$$\frac{3}{11200000}d^{2}-\frac{1}{1000000}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{3}{11200000} for a, 0 for b, and -\frac{1}{1000000} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$d=\frac{0±\sqrt{0^{2}-4\times \frac{3}{11200000}\left(-\frac{1}{1000000}\right)}}{2\times \frac{3}{11200000}}$$

Square 0.

$$d=\frac{0±\sqrt{-4\times \frac{3}{11200000}\left(-\frac{1}{1000000}\right)}}{2\times \frac{3}{11200000}}$$

Multiply -4 times \frac{3}{11200000}.

$$d=\frac{0±\sqrt{-\frac{3}{2800000}\left(-\frac{1}{1000000}\right)}}{2\times \frac{3}{11200000}}$$

Multiply -\frac{3}{2800000} times -\frac{1}{1000000} by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$d=\frac{0±\sqrt{\frac{3}{2800000000000}}}{2\times \frac{3}{11200000}}$$

Take the square root of \frac{3}{2800000000000}.

$$d=\frac{0±\frac{\sqrt{210}}{14000000}}{2\times \frac{3}{11200000}}$$

Multiply 2 times \frac{3}{11200000}.

$$d=\frac{0±\frac{\sqrt{210}}{14000000}}{\frac{3}{5600000}}$$

Now solve the equation d=\frac{0±\frac{\sqrt{210}}{14000000}}{\frac{3}{5600000}} when ± is plus.

$$d=\frac{2\sqrt{210}}{15}$$

Now solve the equation d=\frac{0±\frac{\sqrt{210}}{14000000}}{\frac{3}{5600000}} when ± is minus.

$$d=-\frac{2\sqrt{210}}{15}$$

The equation is now solved.

$$d=\frac{2\sqrt{210}}{15} d=-\frac{2\sqrt{210}}{15}$$