m^2+500m+100=0

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Solution for m^2+500m+100=0 equation: 


Simplifying
m2 + 500m + 100 = 0

Reorder the terms:
100 + 500m + m2 = 0

Solving
100 + 500m + m2 = 0

Solving for variable 'm'.

Begin completing the square.

Move the constant term to the right:

Add '-100' to each side of the equation.
100 + 500m + -100 + m2 = 0 + -100

Reorder the terms:
100 + -100 + 500m + m2 = 0 + -100

Combine like terms: 100 + -100 = 0
0 + 500m + m2 = 0 + -100
500m + m2 = 0 + -100

Combine like terms: 0 + -100 = -100
500m + m2 = -100

The m term is 500m.  Take half its coefficient (250).
Square it (62500) and add it to both sides.

Add '62500' to each side of the equation.
500m + 62500 + m2 = -100 + 62500

Reorder the terms:
62500 + 500m + m2 = -100 + 62500

Combine like terms: -100 + 62500 = 62400
62500 + 500m + m2 = 62400

Factor a perfect square on the left side:
(m + 250)(m + 250) = 62400

Calculate the square root of the right side: 249.799919936

Break this problem into two subproblems by setting 
(m + 250) equal to 249.799919936 and -249.799919936.


Subproblem 1
m + 250 = 249.799919936

Simplifying
m + 250 = 249.799919936

Reorder the terms:
250 + m = 249.799919936

Solving
250 + m = 249.799919936

Solving for variable 'm'.

Move all terms containing m to the left, all other terms to the right.

Add '-250' to each side of the equation.
250 + -250 + m = 249.799919936 + -250

Combine like terms: 250 + -250 = 0
0 + m = 249.799919936 + -250
m = 249.799919936 + -250

Combine like terms: 249.799919936 + -250 = -0.200080064
m = -0.200080064

Simplifying
m = -0.200080064


Subproblem 2
m + 250 = -249.799919936

Simplifying
m + 250 = -249.799919936

Reorder the terms:
250 + m = -249.799919936

Solving
250 + m = -249.799919936

Solving for variable 'm'.

Move all terms containing m to the left, all other terms to the right.

Add '-250' to each side of the equation.
250 + -250 + m = -249.799919936 + -250

Combine like terms: 250 + -250 = 0
0 + m = -249.799919936 + -250
m = -249.799919936 + -250

Combine like terms: -249.799919936 + -250 = -499.799919936
m = -499.799919936

Simplifying
m = -499.799919936


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {-0.200080064, -499.799919936}

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