m^2-14m-13=0

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Solution for m^2-14m-13=0 equation: 


Simplifying
m2 + -14m + -13 = 0

Reorder the terms:
-13 + -14m + m2 = 0

Solving
-13 + -14m + m2 = 0

Solving for variable 'm'.

Begin completing the square.

Move the constant term to the right:

Add '13' to each side of the equation.
-13 + -14m + 13 + m2 = 0 + 13

Reorder the terms:
-13 + 13 + -14m + m2 = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -14m + m2 = 0 + 13
-14m + m2 = 0 + 13

Combine like terms: 0 + 13 = 13
-14m + m2 = 13

The m term is -14m.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14m + 49 + m2 = 13 + 49

Reorder the terms:
49 + -14m + m2 = 13 + 49

Combine like terms: 13 + 49 = 62
49 + -14m + m2 = 62

Factor a perfect square on the left side:
(m + -7)(m + -7) = 62

Calculate the square root of the right side: 7.874007874

Break this problem into two subproblems by setting 
(m + -7) equal to 7.874007874 and -7.874007874.


Subproblem 1
m + -7 = 7.874007874

Simplifying
m + -7 = 7.874007874

Reorder the terms:
-7 + m = 7.874007874

Solving
-7 + m = 7.874007874

Solving for variable 'm'.

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

Add '7' to each side of the equation.
-7 + 7 + m = 7.874007874 + 7

Combine like terms: -7 + 7 = 0
0 + m = 7.874007874 + 7
m = 7.874007874 + 7

Combine like terms: 7.874007874 + 7 = 14.874007874
m = 14.874007874

Simplifying
m = 14.874007874


Subproblem 2
m + -7 = -7.874007874

Simplifying
m + -7 = -7.874007874

Reorder the terms:
-7 + m = -7.874007874

Solving
-7 + m = -7.874007874

Solving for variable 'm'.

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

Add '7' to each side of the equation.
-7 + 7 + m = -7.874007874 + 7

Combine like terms: -7 + 7 = 0
0 + m = -7.874007874 + 7
m = -7.874007874 + 7

Combine like terms: -7.874007874 + 7 = -0.874007874
m = -0.874007874

Simplifying
m = -0.874007874


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {14.874007874, -0.874007874}

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