m^2+9.9m+7=0

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Solution for m^2+9.9m+7=0 equation: 


Simplifying
m2 + 9.9m + 7 = 0

Reorder the terms:
7 + 9.9m + m2 = 0

Solving
7 + 9.9m + m2 = 0

Solving for variable 'm'.

Begin completing the square.

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + 9.9m + -7 + m2 = 0 + -7

Reorder the terms:
7 + -7 + 9.9m + m2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 9.9m + m2 = 0 + -7
9.9m + m2 = 0 + -7

Combine like terms: 0 + -7 = -7
9.9m + m2 = -7

The m term is 9.9m.  Take half its coefficient (4.95).
Square it (24.5025) and add it to both sides.

Add '24.5025' to each side of the equation.
9.9m + 24.5025 + m2 = -7 + 24.5025

Reorder the terms:
24.5025 + 9.9m + m2 = -7 + 24.5025

Combine like terms: -7 + 24.5025 = 17.5025
24.5025 + 9.9m + m2 = 17.5025

Factor a perfect square on the left side:
(m + 4.95)(m + 4.95) = 17.5025

Calculate the square root of the right side: 4.183598929

Break this problem into two subproblems by setting 
(m + 4.95) equal to 4.183598929 and -4.183598929.


Subproblem 1
m + 4.95 = 4.183598929

Simplifying
m + 4.95 = 4.183598929

Reorder the terms:
4.95 + m = 4.183598929

Solving
4.95 + m = 4.183598929

Solving for variable 'm'.

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

Add '-4.95' to each side of the equation.
4.95 + -4.95 + m = 4.183598929 + -4.95

Combine like terms: 4.95 + -4.95 = 0.00
0.00 + m = 4.183598929 + -4.95
m = 4.183598929 + -4.95

Combine like terms: 4.183598929 + -4.95 = -0.766401071
m = -0.766401071

Simplifying
m = -0.766401071


Subproblem 2
m + 4.95 = -4.183598929

Simplifying
m + 4.95 = -4.183598929

Reorder the terms:
4.95 + m = -4.183598929

Solving
4.95 + m = -4.183598929

Solving for variable 'm'.

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

Add '-4.95' to each side of the equation.
4.95 + -4.95 + m = -4.183598929 + -4.95

Combine like terms: 4.95 + -4.95 = 0.00
0.00 + m = -4.183598929 + -4.95
m = -4.183598929 + -4.95

Combine like terms: -4.183598929 + -4.95 = -9.133598929
m = -9.133598929

Simplifying
m = -9.133598929


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {-0.766401071, -9.133598929}

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