m^2+7m+1=0

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Solution for m^2+7m+1=0 equation: 


Simplifying
m2 + 7m + 1 = 0

Reorder the terms:
1 + 7m + m2 = 0

Solving
1 + 7m + m2 = 0

Solving for variable 'm'.

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 7m + -1 + m2 = 0 + -1

Reorder the terms:
1 + -1 + 7m + m2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 7m + m2 = 0 + -1
7m + m2 = 0 + -1

Combine like terms: 0 + -1 = -1
7m + m2 = -1

The m term is 7m.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7m + 12.25 + m2 = -1 + 12.25

Reorder the terms:
12.25 + 7m + m2 = -1 + 12.25

Combine like terms: -1 + 12.25 = 11.25
12.25 + 7m + m2 = 11.25

Factor a perfect square on the left side:
(m + 3.5)(m + 3.5) = 11.25

Calculate the square root of the right side: 3.354101966

Break this problem into two subproblems by setting 
(m + 3.5) equal to 3.354101966 and -3.354101966.


Subproblem 1
m + 3.5 = 3.354101966

Simplifying
m + 3.5 = 3.354101966

Reorder the terms:
3.5 + m = 3.354101966

Solving
3.5 + m = 3.354101966

Solving for variable 'm'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + m = 3.354101966 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + m = 3.354101966 + -3.5
m = 3.354101966 + -3.5

Combine like terms: 3.354101966 + -3.5 = -0.145898034
m = -0.145898034

Simplifying
m = -0.145898034


Subproblem 2
m + 3.5 = -3.354101966

Simplifying
m + 3.5 = -3.354101966

Reorder the terms:
3.5 + m = -3.354101966

Solving
3.5 + m = -3.354101966

Solving for variable 'm'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + m = -3.354101966 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + m = -3.354101966 + -3.5
m = -3.354101966 + -3.5

Combine like terms: -3.354101966 + -3.5 = -6.854101966
m = -6.854101966

Simplifying
m = -6.854101966


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {-0.145898034, -6.854101966}

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