Solve 20=910^9610^-6310^-6/R^2

$$20 = \frac{ 9 { 10 }^{ 9 } 6 { 10 }^{ -6 } 3 { 10 }^{ -6 } }{ { R }^{ 2 } }$$

Solve for R

$$R=\frac{9}{100}=0.09$$

$$R=-\frac{9}{100}=-0.09$$

Steps Using Difference of Squares

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

$$20R^{2}=9\times 10^{9}\times 6\times 10^{-6}\times 3\times 10^{-6}$$

To multiply powers of the same base, add their exponents. Add 9 and -6 to get 3.

$$20R^{2}=9\times 10^{3}\times 6\times 3\times 10^{-6}$$

To multiply powers of the same base, add their exponents. Add 3 and -6 to get -3.

$$20R^{2}=9\times 10^{-3}\times 6\times 3$$

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

$$20R^{2}=9\times \frac{1}{1000}\times 6\times 3$$

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

$$20R^{2}=\frac{9}{1000}\times 6\times 3$$

Multiply \frac{9}{1000} and 6 to get \frac{27}{500}.

$$20R^{2}=\frac{27}{500}\times 3$$

Multiply \frac{27}{500} and 3 to get \frac{81}{500}.

$$20R^{2}=\frac{81}{500}$$

Subtract \frac{81}{500} from both sides.

$$20R^{2}-\frac{81}{500}=0$$

Multiply both sides by 500.

$$10000R^{2}-81=0$$

Consider 10000R^{2}-81. Rewrite 10000R^{2}-81 as \left(100R\right)^{2}-9^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(100R-9\right)\left(100R+9\right)=0$$

To find equation solutions, solve 100R-9=0 and 100R+9=0.

$$R=\frac{9}{100} R=-\frac{9}{100}$$

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}.

$$20R^{2}=9\times 10^{9}\times 6\times 10^{-6}\times 3\times 10^{-6}$$

To multiply powers of the same base, add their exponents. Add 9 and -6 to get 3.

$$20R^{2}=9\times 10^{3}\times 6\times 3\times 10^{-6}$$

To multiply powers of the same base, add their exponents. Add 3 and -6 to get -3.

$$20R^{2}=9\times 10^{-3}\times 6\times 3$$

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

$$20R^{2}=9\times \frac{1}{1000}\times 6\times 3$$

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

$$20R^{2}=\frac{9}{1000}\times 6\times 3$$

Multiply \frac{9}{1000} and 6 to get \frac{27}{500}.

$$20R^{2}=\frac{27}{500}\times 3$$

Multiply \frac{27}{500} and 3 to get \frac{81}{500}.

$$20R^{2}=\frac{81}{500}$$

Divide both sides by 20.

$$R^{2}=\frac{\frac{81}{500}}{20}$$

Express \frac{\frac{81}{500}}{20} as a single fraction.

$$R^{2}=\frac{81}{500\times 20}$$

Multiply 500 and 20 to get 10000.

$$R^{2}=\frac{81}{10000}$$

Take the square root of both sides of the equation.

$$R=\frac{9}{100} R=-\frac{9}{100}$$

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}.

$$20R^{2}=9\times 10^{9}\times 6\times 10^{-6}\times 3\times 10^{-6}$$

To multiply powers of the same base, add their exponents. Add 9 and -6 to get 3.

$$20R^{2}=9\times 10^{3}\times 6\times 3\times 10^{-6}$$

To multiply powers of the same base, add their exponents. Add 3 and -6 to get -3.

$$20R^{2}=9\times 10^{-3}\times 6\times 3$$

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

$$20R^{2}=9\times \frac{1}{1000}\times 6\times 3$$

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

$$20R^{2}=\frac{9}{1000}\times 6\times 3$$

Multiply \frac{9}{1000} and 6 to get \frac{27}{500}.

$$20R^{2}=\frac{27}{500}\times 3$$

Multiply \frac{27}{500} and 3 to get \frac{81}{500}.

$$20R^{2}=\frac{81}{500}$$

Subtract \frac{81}{500} from both sides.

$$20R^{2}-\frac{81}{500}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 20 for a, 0 for b, and -\frac{81}{500} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$R=\frac{0±\sqrt{0^{2}-4\times 20\left(-\frac{81}{500}\right)}}{2\times 20}$$

Square 0.

$$R=\frac{0±\sqrt{-4\times 20\left(-\frac{81}{500}\right)}}{2\times 20}$$

Multiply -4 times 20.

$$R=\frac{0±\sqrt{-80\left(-\frac{81}{500}\right)}}{2\times 20}$$

Multiply -80 times -\frac{81}{500}.

$$R=\frac{0±\sqrt{\frac{324}{25}}}{2\times 20}$$

Take the square root of \frac{324}{25}.

$$R=\frac{0±\frac{18}{5}}{2\times 20}$$

Multiply 2 times 20.

$$R=\frac{0±\frac{18}{5}}{40}$$

Now solve the equation R=\frac{0±\frac{18}{5}}{40} when ± is plus.

$$R=\frac{9}{100}$$

Now solve the equation R=\frac{0±\frac{18}{5}}{40} when ± is minus.

$$R=-\frac{9}{100}$$

The equation is now solved.

$$R=\frac{9}{100} R=-\frac{9}{100}$$