Solve 20=9.1^9610^-6310^-6/R^2

$$20 = \frac{ { 9.1 }^{ 9 } 6 { 10 }^{ -6 } 3 { 10 }^{ -6 } }{ { R }^{ 2 } }$$

Solve for R

$$R=\frac{205724883\sqrt{91}}{100000000000}\approx 0.019624903$$

$$R=-\frac{205724883\sqrt{91}}{100000000000}\approx -0.019624903$$

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}.

$$20R^{2}=9.1^{9}\times 6\times 10^{-6}\times 3\times 10^{-6}$$

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

$$20R^{2}=9.1^{9}\times 6\times 10^{-12}\times 3$$

Calculate 9.1 to the power of 9 and get 427929800.129788411.

$$20R^{2}=427929800.129788411\times 6\times 10^{-12}\times 3$$

Multiply 427929800.129788411 and 6 to get 2567578800.778730466.

$$20R^{2}=2567578800.778730466\times 10^{-12}\times 3$$

Calculate 10 to the power of -12 and get \frac{1}{1000000000000}.

$$20R^{2}=2567578800.778730466\times \frac{1}{1000000000000}\times 3$$

Multiply 2567578800.778730466 and \frac{1}{1000000000000} to get \frac{1283789400389365233}{500000000000000000000}.

$$20R^{2}=\frac{1283789400389365233}{500000000000000000000}\times 3$$

Multiply \frac{1283789400389365233}{500000000000000000000} and 3 to get \frac{3851368201168095699}{500000000000000000000}.

$$20R^{2}=\frac{3851368201168095699}{500000000000000000000}$$

Divide both sides by 20.

$$R^{2}=\frac{\frac{3851368201168095699}{500000000000000000000}}{20}$$

Express \frac{\frac{3851368201168095699}{500000000000000000000}}{20} as a single fraction.

$$R^{2}=\frac{3851368201168095699}{500000000000000000000\times 20}$$

Multiply 500000000000000000000 and 20 to get 10000000000000000000000.

$$R^{2}=\frac{3851368201168095699}{10000000000000000000000}$$

Take the square root of both sides of the equation.

$$R=\frac{205724883\sqrt{91}}{100000000000} R=-\frac{205724883\sqrt{91}}{100000000000}$$

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}.

$$20R^{2}=9.1^{9}\times 6\times 10^{-6}\times 3\times 10^{-6}$$

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

$$20R^{2}=9.1^{9}\times 6\times 10^{-12}\times 3$$

Calculate 9.1 to the power of 9 and get 427929800.129788411.

$$20R^{2}=427929800.129788411\times 6\times 10^{-12}\times 3$$

Multiply 427929800.129788411 and 6 to get 2567578800.778730466.

$$20R^{2}=2567578800.778730466\times 10^{-12}\times 3$$

Calculate 10 to the power of -12 and get \frac{1}{1000000000000}.

$$20R^{2}=2567578800.778730466\times \frac{1}{1000000000000}\times 3$$

Multiply 2567578800.778730466 and \frac{1}{1000000000000} to get \frac{1283789400389365233}{500000000000000000000}.

$$20R^{2}=\frac{1283789400389365233}{500000000000000000000}\times 3$$

Multiply \frac{1283789400389365233}{500000000000000000000} and 3 to get \frac{3851368201168095699}{500000000000000000000}.

$$20R^{2}=\frac{3851368201168095699}{500000000000000000000}$$

Subtract \frac{3851368201168095699}{500000000000000000000} from both sides.

$$20R^{2}-\frac{3851368201168095699}{500000000000000000000}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 20 for a, 0 for b, and -\frac{3851368201168095699}{500000000000000000000} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$R=\frac{0±\sqrt{0^{2}-4\times 20\left(-\frac{3851368201168095699}{500000000000000000000}\right)}}{2\times 20}$$

Square 0.

$$R=\frac{0±\sqrt{-4\times 20\left(-\frac{3851368201168095699}{500000000000000000000}\right)}}{2\times 20}$$

Multiply -4 times 20.

$$R=\frac{0±\sqrt{-80\left(-\frac{3851368201168095699}{500000000000000000000}\right)}}{2\times 20}$$

Multiply -80 times -\frac{3851368201168095699}{500000000000000000000}.

$$R=\frac{0±\sqrt{\frac{3851368201168095699}{6250000000000000000}}}{2\times 20}$$

Take the square root of \frac{3851368201168095699}{6250000000000000000}.

$$R=\frac{0±\frac{205724883\sqrt{91}}{2500000000}}{2\times 20}$$

Multiply 2 times 20.

$$R=\frac{0±\frac{205724883\sqrt{91}}{2500000000}}{40}$$

Now solve the equation R=\frac{0±\frac{205724883\sqrt{91}}{2500000000}}{40} when ± is plus.

$$R=\frac{205724883\sqrt{91}}{100000000000}$$

Now solve the equation R=\frac{0±\frac{205724883\sqrt{91}}{2500000000}}{40} when ± is minus.

$$R=-\frac{205724883\sqrt{91}}{100000000000}$$

The equation is now solved.

$$R=\frac{205724883\sqrt{91}}{100000000000} R=-\frac{205724883\sqrt{91}}{100000000000}$$