6m^2+17m+2=0

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Solution for 6m^2+17m+2=0 equation: 


Simplifying
6m2 + 17m + 2 = 0

Reorder the terms:
2 + 17m + 6m2 = 0

Solving
2 + 17m + 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 + 2.833333333m + m2 = 0

Move the constant term to the right:

Add '-0.3333333333' to each side of the equation.
0.3333333333 + 2.833333333m + -0.3333333333 + m2 = 0 + -0.3333333333

Reorder the terms:
0.3333333333 + -0.3333333333 + 2.833333333m + m2 = 0 + -0.3333333333

Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000
0.0000000000 + 2.833333333m + m2 = 0 + -0.3333333333
2.833333333m + m2 = 0 + -0.3333333333

Combine like terms: 0 + -0.3333333333 = -0.3333333333
2.833333333m + m2 = -0.3333333333

The m term is 2.833333333m.  Take half its coefficient (1.416666667).
Square it (2.006944445) and add it to both sides.

Add '2.006944445' to each side of the equation.
2.833333333m + 2.006944445 + m2 = -0.3333333333 + 2.006944445

Reorder the terms:
2.006944445 + 2.833333333m + m2 = -0.3333333333 + 2.006944445

Combine like terms: -0.3333333333 + 2.006944445 = 1.6736111117
2.006944445 + 2.833333333m + m2 = 1.6736111117

Factor a perfect square on the left side:
(m + 1.416666667)(m + 1.416666667) = 1.6736111117

Calculate the square root of the right side: 1.293681225

Break this problem into two subproblems by setting 
(m + 1.416666667) equal to 1.293681225 and -1.293681225.


Subproblem 1
m + 1.416666667 = 1.293681225

Simplifying
m + 1.416666667 = 1.293681225

Reorder the terms:
1.416666667 + m = 1.293681225

Solving
1.416666667 + m = 1.293681225

Solving for variable 'm'.

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

Add '-1.416666667' to each side of the equation.
1.416666667 + -1.416666667 + m = 1.293681225 + -1.416666667

Combine like terms: 1.416666667 + -1.416666667 = 0.000000000
0.000000000 + m = 1.293681225 + -1.416666667
m = 1.293681225 + -1.416666667

Combine like terms: 1.293681225 + -1.416666667 = -0.122985442
m = -0.122985442

Simplifying
m = -0.122985442


Subproblem 2
m + 1.416666667 = -1.293681225

Simplifying
m + 1.416666667 = -1.293681225

Reorder the terms:
1.416666667 + m = -1.293681225

Solving
1.416666667 + m = -1.293681225

Solving for variable 'm'.

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

Add '-1.416666667' to each side of the equation.
1.416666667 + -1.416666667 + m = -1.293681225 + -1.416666667

Combine like terms: 1.416666667 + -1.416666667 = 0.000000000
0.000000000 + m = -1.293681225 + -1.416666667
m = -1.293681225 + -1.416666667

Combine like terms: -1.293681225 + -1.416666667 = -2.710347892
m = -2.710347892

Simplifying
m = -2.710347892


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {-0.122985442, -2.710347892}

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