Solve m=-2+sqrt{1/0.998^2+0.998^2/1+2}

$$m = -2+ \sqrt{ \frac{ 1 }{ { 0.998 }^{ 2 } } + \frac{ { 0.998 }^{ 2 } }{ 1 } +2 }$$

Solve for m

$$m=\frac{1}{249500}\approx 0.000004008$$

Steps for Solving Linear Equation

Calculate 0.998 to the power of 2 and get 0.996004.

$$m=-2+\sqrt{\frac{1}{0.996004}+\frac{0.998^{2}}{1}+2}$$

Expand \frac{1}{0.996004} by multiplying both numerator and the denominator by 1000000.

$$m=-2+\sqrt{\frac{1000000}{996004}+\frac{0.998^{2}}{1}+2}$$

Reduce the fraction \frac{1000000}{996004} to lowest terms by extracting and canceling out 4.

$$m=-2+\sqrt{\frac{250000}{249001}+\frac{0.998^{2}}{1}+2}$$

Calculate 0.998 to the power of 2 and get 0.996004.

$$m=-2+\sqrt{\frac{250000}{249001}+\frac{0.996004}{1}+2}$$

Anything divided by one gives itself.

$$m=-2+\sqrt{\frac{250000}{249001}+0.996004+2}$$

Convert decimal number 0.996004 to fraction \frac{996004}{1000000}. Reduce the fraction \frac{996004}{1000000} to lowest terms by extracting and canceling out 4.

$$m=-2+\sqrt{\frac{250000}{249001}+\frac{249001}{250000}+2}$$

Least common multiple of 249001 and 250000 is 62250250000. Convert \frac{250000}{249001} and \frac{249001}{250000} to fractions with denominator 62250250000.

$$m=-2+\sqrt{\frac{62500000000}{62250250000}+\frac{62001498001}{62250250000}+2}$$

Since \frac{62500000000}{62250250000} and \frac{62001498001}{62250250000} have the same denominator, add them by adding their numerators.

$$m=-2+\sqrt{\frac{62500000000+62001498001}{62250250000}+2}$$

Add 62500000000 and 62001498001 to get 124501498001.

$$m=-2+\sqrt{\frac{124501498001}{62250250000}+2}$$

Convert 2 to fraction \frac{124500500000}{62250250000}.

$$m=-2+\sqrt{\frac{124501498001}{62250250000}+\frac{124500500000}{62250250000}}$$

Since \frac{124501498001}{62250250000} and \frac{124500500000}{62250250000} have the same denominator, add them by adding their numerators.

$$m=-2+\sqrt{\frac{124501498001+124500500000}{62250250000}}$$

Add 124501498001 and 124500500000 to get 249001998001.

$$m=-2+\sqrt{\frac{249001998001}{62250250000}}$$

Rewrite the square root of the division \frac{249001998001}{62250250000} as the division of square roots \frac{\sqrt{249001998001}}{\sqrt{62250250000}}. Take the square root of both numerator and denominator.

$$m=-2+\frac{499001}{249500}$$

Convert -2 to fraction -\frac{499000}{249500}.

$$m=-\frac{499000}{249500}+\frac{499001}{249500}$$

Since -\frac{499000}{249500} and \frac{499001}{249500} have the same denominator, add them by adding their numerators.

$$m=\frac{-499000+499001}{249500}$$

Add -499000 and 499001 to get 1.

$$m=\frac{1}{249500}$$

Assign m

$$m≔\frac{1}{249500}$$