3m^2+17m+6=0

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Solution for 3m^2+17m+6=0 equation: 


Simplifying
3m2 + 17m + 6 = 0

Reorder the terms:
6 + 17m + 3m2 = 0

Solving
6 + 17m + 3m2 = 0

Solving for variable 'm'.

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

Divide each side by '3'.
2 + 5.666666667m + m2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 5.666666667m + -2 + m2 = 0 + -2

Reorder the terms:
2 + -2 + 5.666666667m + m2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 5.666666667m + m2 = 0 + -2
5.666666667m + m2 = 0 + -2

Combine like terms: 0 + -2 = -2
5.666666667m + m2 = -2

The m term is 5.666666667m.  Take half its coefficient (2.833333334).
Square it (8.027777782) and add it to both sides.

Add '8.027777782' to each side of the equation.
5.666666667m + 8.027777782 + m2 = -2 + 8.027777782

Reorder the terms:
8.027777782 + 5.666666667m + m2 = -2 + 8.027777782

Combine like terms: -2 + 8.027777782 = 6.027777782
8.027777782 + 5.666666667m + m2 = 6.027777782

Factor a perfect square on the left side:
(m + 2.833333334)(m + 2.833333334) = 6.027777782

Calculate the square root of the right side: 2.455153311

Break this problem into two subproblems by setting 
(m + 2.833333334) equal to 2.455153311 and -2.455153311.


Subproblem 1
m + 2.833333334 = 2.455153311

Simplifying
m + 2.833333334 = 2.455153311

Reorder the terms:
2.833333334 + m = 2.455153311

Solving
2.833333334 + m = 2.455153311

Solving for variable 'm'.

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

Add '-2.833333334' to each side of the equation.
2.833333334 + -2.833333334 + m = 2.455153311 + -2.833333334

Combine like terms: 2.833333334 + -2.833333334 = 0.000000000
0.000000000 + m = 2.455153311 + -2.833333334
m = 2.455153311 + -2.833333334

Combine like terms: 2.455153311 + -2.833333334 = -0.378180023
m = -0.378180023

Simplifying
m = -0.378180023


Subproblem 2
m + 2.833333334 = -2.455153311

Simplifying
m + 2.833333334 = -2.455153311

Reorder the terms:
2.833333334 + m = -2.455153311

Solving
2.833333334 + m = -2.455153311

Solving for variable 'm'.

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

Add '-2.833333334' to each side of the equation.
2.833333334 + -2.833333334 + m = -2.455153311 + -2.833333334

Combine like terms: 2.833333334 + -2.833333334 = 0.000000000
0.000000000 + m = -2.455153311 + -2.833333334
m = -2.455153311 + -2.833333334

Combine like terms: -2.455153311 + -2.833333334 = -5.288486645
m = -5.288486645

Simplifying
m = -5.288486645


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {-0.378180023, -5.288486645}

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