m^2+20m+100=50

Solution for m^2+20m+100=50 equation:

Simplifying
m2 + 20m + 100 = 50

Reorder the terms:
100 + 20m + m2 = 50

Solving
100 + 20m + m2 = 50

Solving for variable 'm'.

Reorder the terms:
100 + -50 + 20m + m2 = 50 + -50

Combine like terms: 100 + -50 = 50
50 + 20m + m2 = 50 + -50

Combine like terms: 50 + -50 = 0
50 + 20m + m2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-50' to each side of the equation.
50 + 20m + -50 + m2 = 0 + -50

Reorder the terms:
50 + -50 + 20m + m2 = 0 + -50

Combine like terms: 50 + -50 = 0
0 + 20m + m2 = 0 + -50
20m + m2 = 0 + -50

Combine like terms: 0 + -50 = -50
20m + m2 = -50

The m term is 20m.  Take half its coefficient (10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
20m + 100 + m2 = -50 + 100

Reorder the terms:
100 + 20m + m2 = -50 + 100

Combine like terms: -50 + 100 = 50
100 + 20m + m2 = 50

Factor a perfect square on the left side:
(m + 10)(m + 10) = 50

Calculate the square root of the right side: 7.071067812

Break this problem into two subproblems by setting 
(m + 10) equal to 7.071067812 and -7.071067812.

Subproblem 1
m + 10 = 7.071067812

Simplifying
m + 10 = 7.071067812

Reorder the terms:
10 + m = 7.071067812

Solving
10 + m = 7.071067812

Solving for variable 'm'.

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

Add '-10' to each side of the equation.
10 + -10 + m = 7.071067812 + -10

Combine like terms: 10 + -10 = 0
0 + m = 7.071067812 + -10
m = 7.071067812 + -10

Combine like terms: 7.071067812 + -10 = -2.928932188
m = -2.928932188

Simplifying
m = -2.928932188

Subproblem 2
m + 10 = -7.071067812

Simplifying
m + 10 = -7.071067812

Reorder the terms:
10 + m = -7.071067812

Solving
10 + m = -7.071067812

Solving for variable 'm'.

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

Add '-10' to each side of the equation.
10 + -10 + m = -7.071067812 + -10

Combine like terms: 10 + -10 = 0
0 + m = -7.071067812 + -10
m = -7.071067812 + -10

Combine like terms: -7.071067812 + -10 = -17.071067812
m = -17.071067812

Simplifying
m = -17.071067812

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {-2.928932188, -17.071067812}