m^2-4m-34=0

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Solution for m^2-4m-34=0 equation: 


Simplifying
m2 + -4m + -34 = 0

Reorder the terms:
-34 + -4m + m2 = 0

Solving
-34 + -4m + 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 + -4m + 34 + m2 = 0 + 34

Reorder the terms:
-34 + 34 + -4m + m2 = 0 + 34

Combine like terms: -34 + 34 = 0
0 + -4m + m2 = 0 + 34
-4m + m2 = 0 + 34

Combine like terms: 0 + 34 = 34
-4m + m2 = 34

The m term is -4m.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4m + 4 + m2 = 34 + 4

Reorder the terms:
4 + -4m + m2 = 34 + 4

Combine like terms: 34 + 4 = 38
4 + -4m + m2 = 38

Factor a perfect square on the left side:
(m + -2)(m + -2) = 38

Calculate the square root of the right side: 6.164414003

Break this problem into two subproblems by setting 
(m + -2) equal to 6.164414003 and -6.164414003.


Subproblem 1
m + -2 = 6.164414003

Simplifying
m + -2 = 6.164414003

Reorder the terms:
-2 + m = 6.164414003

Solving
-2 + m = 6.164414003

Solving for variable 'm'.

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

Add '2' to each side of the equation.
-2 + 2 + m = 6.164414003 + 2

Combine like terms: -2 + 2 = 0
0 + m = 6.164414003 + 2
m = 6.164414003 + 2

Combine like terms: 6.164414003 + 2 = 8.164414003
m = 8.164414003

Simplifying
m = 8.164414003


Subproblem 2
m + -2 = -6.164414003

Simplifying
m + -2 = -6.164414003

Reorder the terms:
-2 + m = -6.164414003

Solving
-2 + m = -6.164414003

Solving for variable 'm'.

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

Add '2' to each side of the equation.
-2 + 2 + m = -6.164414003 + 2

Combine like terms: -2 + 2 = 0
0 + m = -6.164414003 + 2
m = -6.164414003 + 2

Combine like terms: -6.164414003 + 2 = -4.164414003
m = -4.164414003

Simplifying
m = -4.164414003


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {8.164414003, -4.164414003}

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