Solve 0.2=9*10^9*0.4*10^-6*0.8*10^-6/r^2

$$0.2 = 9 \times 10 ^ { 9 } \times \frac { 0.4 \times 10 ^ { - 6 } \times 0.8 \times 10 ^ { - 6 } } { r ^ { 2 } }$$

Solve for r

$$r=0.12$$

$$r=-0.12$$

Steps by Finding Square Root

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

$$0.2r^{2}=9\times 10^{9}\times 0.4\times 10^{-6}\times 0.8\times 10^{-6}$$

To multiply powers of the same base, add their exponents. Add -6 and -6 to get -12.

$$0.2r^{2}=9\times 10^{9}\times 0.4\times 10^{-12}\times 0.8$$

To multiply powers of the same base, add their exponents. Add 9 and -12 to get -3.

$$0.2r^{2}=9\times 10^{-3}\times 0.4\times 0.8$$

Calculate 10 to the power of -3 and get \frac{1}{1000}.

$$0.2r^{2}=9\times \frac{1}{1000}\times 0.4\times 0.8$$

Multiply 9 and \frac{1}{1000} to get \frac{9}{1000}.

$$0.2r^{2}=\frac{9}{1000}\times 0.4\times 0.8$$

Multiply \frac{9}{1000} and 0.4 to get \frac{9}{2500}.

$$0.2r^{2}=\frac{9}{2500}\times 0.8$$

Multiply \frac{9}{2500} and 0.8 to get \frac{9}{3125}.

$$0.2r^{2}=\frac{9}{3125}$$

Divide both sides by 0.2.

$$r^{2}=\frac{\frac{9}{3125}}{0.2}$$

Express \frac{\frac{9}{3125}}{0.2} as a single fraction.

$$r^{2}=\frac{9}{3125\times 0.2}$$

Multiply 3125 and 0.2 to get 625.

$$r^{2}=\frac{9}{625}$$

Take the square root of both sides of the equation.

$$r=\frac{3}{25} r=-\frac{3}{25}$$

Steps Using the Quadratic Formula

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

$$0.2r^{2}=9\times 10^{9}\times 0.4\times 10^{-6}\times 0.8\times 10^{-6}$$

To multiply powers of the same base, add their exponents. Add -6 and -6 to get -12.

$$0.2r^{2}=9\times 10^{9}\times 0.4\times 10^{-12}\times 0.8$$

To multiply powers of the same base, add their exponents. Add 9 and -12 to get -3.

$$0.2r^{2}=9\times 10^{-3}\times 0.4\times 0.8$$

Calculate 10 to the power of -3 and get \frac{1}{1000}.

$$0.2r^{2}=9\times \frac{1}{1000}\times 0.4\times 0.8$$

Multiply 9 and \frac{1}{1000} to get \frac{9}{1000}.

$$0.2r^{2}=\frac{9}{1000}\times 0.4\times 0.8$$

Multiply \frac{9}{1000} and 0.4 to get \frac{9}{2500}.

$$0.2r^{2}=\frac{9}{2500}\times 0.8$$

Multiply \frac{9}{2500} and 0.8 to get \frac{9}{3125}.

$$0.2r^{2}=\frac{9}{3125}$$

Subtract \frac{9}{3125} from both sides.

$$0.2r^{2}-\frac{9}{3125}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 0.2 for a, 0 for b, and -\frac{9}{3125} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$r=\frac{0±\sqrt{0^{2}-4\times 0.2\left(-\frac{9}{3125}\right)}}{2\times 0.2}$$

Square 0.

$$r=\frac{0±\sqrt{-4\times 0.2\left(-\frac{9}{3125}\right)}}{2\times 0.2}$$

Multiply -4 times 0.2.

$$r=\frac{0±\sqrt{-0.8\left(-\frac{9}{3125}\right)}}{2\times 0.2}$$

Multiply -0.8 times -\frac{9}{3125} by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$r=\frac{0±\sqrt{\frac{36}{15625}}}{2\times 0.2}$$

Take the square root of \frac{36}{15625}.

$$r=\frac{0±\frac{6}{125}}{2\times 0.2}$$

Multiply 2 times 0.2.

$$r=\frac{0±\frac{6}{125}}{0.4}$$

Now solve the equation r=\frac{0±\frac{6}{125}}{0.4} when ± is plus.

$$r=\frac{3}{25}$$

Now solve the equation r=\frac{0±\frac{6}{125}}{0.4} when ± is minus.

$$r=-\frac{3}{25}$$

The equation is now solved.

$$r=\frac{3}{25} r=-\frac{3}{25}$$