m(m+1)=100

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Solution for m(m+1)=100 equation: 


Simplifying
m(m + 1) = 100

Reorder the terms:
m(1 + m) = 100
(1 * m + m * m) = 100
(1m + m2) = 100

Solving
1m + m2 = 100

Solving for variable 'm'.

Reorder the terms:
-100 + 1m + m2 = 100 + -100

Combine like terms: 100 + -100 = 0
-100 + 1m + m2 = 0

Begin completing the square.

Move the constant term to the right:

Add '100' to each side of the equation.
-100 + 1m + 100 + m2 = 0 + 100

Reorder the terms:
-100 + 100 + 1m + m2 = 0 + 100

Combine like terms: -100 + 100 = 0
0 + 1m + m2 = 0 + 100
1m + m2 = 0 + 100

Combine like terms: 0 + 100 = 100
1m + m2 = 100

The m term is 1m.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
m + 0.25 + m2 = 100 + 0.25

Reorder the terms:
0.25 + m + m2 = 100 + 0.25

Combine like terms: 100 + 0.25 = 100.25
0.25 + m + m2 = 100.25

Factor a perfect square on the left side:
(m + 0.5)(m + 0.5) = 100.25

Calculate the square root of the right side: 10.012492197

Break this problem into two subproblems by setting 
(m + 0.5) equal to 10.012492197 and -10.012492197.


Subproblem 1
m + 0.5 = 10.012492197

Simplifying
m + 0.5 = 10.012492197

Reorder the terms:
0.5 + m = 10.012492197

Solving
0.5 + m = 10.012492197

Solving for variable 'm'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + m = 10.012492197 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + m = 10.012492197 + -0.5
m = 10.012492197 + -0.5

Combine like terms: 10.012492197 + -0.5 = 9.512492197
m = 9.512492197

Simplifying
m = 9.512492197


Subproblem 2
m + 0.5 = -10.012492197

Simplifying
m + 0.5 = -10.012492197

Reorder the terms:
0.5 + m = -10.012492197

Solving
0.5 + m = -10.012492197

Solving for variable 'm'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + m = -10.012492197 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + m = -10.012492197 + -0.5
m = -10.012492197 + -0.5

Combine like terms: -10.012492197 + -0.5 = -10.512492197
m = -10.512492197

Simplifying
m = -10.512492197


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {9.512492197, -10.512492197}

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