Solve 1/2*910^2=6.67*10^-11*5.98*10^24/r

$$\frac { 1 } { 2 } \times 910 ^ { 2 } = 6.67 \times 10 ^ { - 11 } \times \frac { 5.98 \times 10 ^ { 24 } } { r }$$

Solve for r

$$r = \frac{613640000000}{637} = 963328100\frac{300}{637} \approx 963328100.470957614$$

Steps for Solving Linear Equation

Variable r cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 2r, the least common multiple of 2,r.

$$\frac{1}{2}\times 910^{2}\times 2r=6.67\times 10^{-11}\times 2\times 5.98\times 10^{24}$$

Calculate 910 to the power of 2 and get 828100.

$$\frac{1}{2}\times 828100\times 2r=6.67\times 10^{-11}\times 2\times 5.98\times 10^{24}$$

Multiply \frac{1}{2} and 828100 to get 414050.

$$414050\times 2r=6.67\times 10^{-11}\times 2\times 5.98\times 10^{24}$$

Multiply 414050 and 2 to get 828100.

$$828100r=6.67\times 10^{-11}\times 2\times 5.98\times 10^{24}$$

To multiply powers of the same base, add their exponents. Add -11 and 24 to get 13.

$$828100r=6.67\times 10^{13}\times 2\times 5.98$$

Calculate 10 to the power of 13 and get 10000000000000.

$$828100r=6.67\times 10000000000000\times 2\times 5.98$$

Multiply 6.67 and 10000000000000 to get 66700000000000.

$$828100r=66700000000000\times 2\times 5.98$$

Multiply 66700000000000 and 2 to get 133400000000000.

$$828100r=133400000000000\times 5.98$$

Multiply 133400000000000 and 5.98 to get 797732000000000.

$$828100r=797732000000000$$

Divide both sides by 828100.

$$r=\frac{797732000000000}{828100}$$

Reduce the fraction \frac{797732000000000}{828100} to lowest terms by extracting and canceling out 1300.

$$r=\frac{613640000000}{637}$$