-m^2-10m-6=0

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Solution for -m^2-10m-6=0 equation: 


Simplifying
-1m2 + -10m + -6 = 0

Reorder the terms:
-6 + -10m + -1m2 = 0

Solving
-6 + -10m + -1m2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(6 + 10m + m2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(6 + 10m + m2)' equal to zero and attempt to solve:

Simplifying
6 + 10m + m2 = 0

Solving
6 + 10m + m2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + 10m + -6 + m2 = 0 + -6

Reorder the terms:
6 + -6 + 10m + m2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 10m + m2 = 0 + -6
10m + m2 = 0 + -6

Combine like terms: 0 + -6 = -6
10m + m2 = -6

The m term is 10m.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10m + 25 + m2 = -6 + 25

Reorder the terms:
25 + 10m + m2 = -6 + 25

Combine like terms: -6 + 25 = 19
25 + 10m + m2 = 19

Factor a perfect square on the left side:
(m + 5)(m + 5) = 19

Calculate the square root of the right side: 4.358898944

Break this problem into two subproblems by setting 
(m + 5) equal to 4.358898944 and -4.358898944.


Subproblem 1
m + 5 = 4.358898944

Simplifying
m + 5 = 4.358898944

Reorder the terms:
5 + m = 4.358898944

Solving
5 + m = 4.358898944

Solving for variable 'm'.

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

Add '-5' to each side of the equation.
5 + -5 + m = 4.358898944 + -5

Combine like terms: 5 + -5 = 0
0 + m = 4.358898944 + -5
m = 4.358898944 + -5

Combine like terms: 4.358898944 + -5 = -0.641101056
m = -0.641101056

Simplifying
m = -0.641101056


Subproblem 2
m + 5 = -4.358898944

Simplifying
m + 5 = -4.358898944

Reorder the terms:
5 + m = -4.358898944

Solving
5 + m = -4.358898944

Solving for variable 'm'.

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

Add '-5' to each side of the equation.
5 + -5 + m = -4.358898944 + -5

Combine like terms: 5 + -5 = 0
0 + m = -4.358898944 + -5
m = -4.358898944 + -5

Combine like terms: -4.358898944 + -5 = -9.358898944
m = -9.358898944

Simplifying
m = -9.358898944


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {-0.641101056, -9.358898944}
Solution
m = {-0.641101056, -9.358898944}

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