6m^2+25m-2=0

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Solution for 6m^2+25m-2=0 equation: 


Simplifying
6m2 + 25m + -2 = 0

Reorder the terms:
-2 + 25m + 6m2 = 0

Solving
-2 + 25m + 6m2 = 0

Solving for variable 'm'.

Begin completing the square.  Divide all terms by
6 the coefficient of the squared term: 

Divide each side by '6'.
-0.3333333333 + 4.166666667m + m2 = 0

Move the constant term to the right:

Add '0.3333333333' to each side of the equation.
-0.3333333333 + 4.166666667m + 0.3333333333 + m2 = 0 + 0.3333333333

Reorder the terms:
-0.3333333333 + 0.3333333333 + 4.166666667m + m2 = 0 + 0.3333333333

Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000
0.0000000000 + 4.166666667m + m2 = 0 + 0.3333333333
4.166666667m + m2 = 0 + 0.3333333333

Combine like terms: 0 + 0.3333333333 = 0.3333333333
4.166666667m + m2 = 0.3333333333

The m term is 4.166666667m.  Take half its coefficient (2.083333334).
Square it (4.340277781) and add it to both sides.

Add '4.340277781' to each side of the equation.
4.166666667m + 4.340277781 + m2 = 0.3333333333 + 4.340277781

Reorder the terms:
4.340277781 + 4.166666667m + m2 = 0.3333333333 + 4.340277781

Combine like terms: 0.3333333333 + 4.340277781 = 4.6736111143
4.340277781 + 4.166666667m + m2 = 4.6736111143

Factor a perfect square on the left side:
(m + 2.083333334)(m + 2.083333334) = 4.6736111143

Calculate the square root of the right side: 2.161853629

Break this problem into two subproblems by setting 
(m + 2.083333334) equal to 2.161853629 and -2.161853629.


Subproblem 1
m + 2.083333334 = 2.161853629

Simplifying
m + 2.083333334 = 2.161853629

Reorder the terms:
2.083333334 + m = 2.161853629

Solving
2.083333334 + m = 2.161853629

Solving for variable 'm'.

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

Add '-2.083333334' to each side of the equation.
2.083333334 + -2.083333334 + m = 2.161853629 + -2.083333334

Combine like terms: 2.083333334 + -2.083333334 = 0.000000000
0.000000000 + m = 2.161853629 + -2.083333334
m = 2.161853629 + -2.083333334

Combine like terms: 2.161853629 + -2.083333334 = 0.078520295
m = 0.078520295

Simplifying
m = 0.078520295


Subproblem 2
m + 2.083333334 = -2.161853629

Simplifying
m + 2.083333334 = -2.161853629

Reorder the terms:
2.083333334 + m = -2.161853629

Solving
2.083333334 + m = -2.161853629

Solving for variable 'm'.

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

Add '-2.083333334' to each side of the equation.
2.083333334 + -2.083333334 + m = -2.161853629 + -2.083333334

Combine like terms: 2.083333334 + -2.083333334 = 0.000000000
0.000000000 + m = -2.161853629 + -2.083333334
m = -2.161853629 + -2.083333334

Combine like terms: -2.161853629 + -2.083333334 = -4.245186963
m = -4.245186963

Simplifying
m = -4.245186963


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {0.078520295, -4.245186963}

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