(m*m)-14m+34=0

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Solution for (m*m)-14m+34=0 equation: 


Simplifying
(m * m) + -14m + 34 = 0

Multiply m * m
(m2) + -14m + 34 = 0
m2 + -14m + 34 = 0

Reorder the terms:
34 + -14m + m2 = 0

Solving
34 + -14m + m2 = 0

Solving for variable 'm'.

Begin completing the square.

Move the constant term to the right:

Add '-34' to each side of the equation.
34 + -14m + -34 + m2 = 0 + -34

Reorder the terms:
34 + -34 + -14m + m2 = 0 + -34

Combine like terms: 34 + -34 = 0
0 + -14m + m2 = 0 + -34
-14m + m2 = 0 + -34

Combine like terms: 0 + -34 = -34
-14m + m2 = -34

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 = -34 + 49

Reorder the terms:
49 + -14m + m2 = -34 + 49

Combine like terms: -34 + 49 = 15
49 + -14m + m2 = 15

Factor a perfect square on the left side:
(m + -7)(m + -7) = 15

Calculate the square root of the right side: 3.872983346

Break this problem into two subproblems by setting 
(m + -7) equal to 3.872983346 and -3.872983346.


Subproblem 1
m + -7 = 3.872983346

Simplifying
m + -7 = 3.872983346

Reorder the terms:
-7 + m = 3.872983346

Solving
-7 + m = 3.872983346

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 = 3.872983346 + 7

Combine like terms: -7 + 7 = 0
0 + m = 3.872983346 + 7
m = 3.872983346 + 7

Combine like terms: 3.872983346 + 7 = 10.872983346
m = 10.872983346

Simplifying
m = 10.872983346


Subproblem 2
m + -7 = -3.872983346

Simplifying
m + -7 = -3.872983346

Reorder the terms:
-7 + m = -3.872983346

Solving
-7 + m = -3.872983346

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 = -3.872983346 + 7

Combine like terms: -7 + 7 = 0
0 + m = -3.872983346 + 7
m = -3.872983346 + 7

Combine like terms: -3.872983346 + 7 = 3.127016654
m = 3.127016654

Simplifying
m = 3.127016654


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {10.872983346, 3.127016654}

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