3m^2+17m+15=0

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Solution for 3m^2+17m+15=0 equation: 


Simplifying
3m2 + 17m + 15 = 0

Reorder the terms:
15 + 17m + 3m2 = 0

Solving
15 + 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'.
5 + 5.666666667m + m2 = 0

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + 5.666666667m + -5 + m2 = 0 + -5

Reorder the terms:
5 + -5 + 5.666666667m + m2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 5.666666667m + m2 = 0 + -5
5.666666667m + m2 = 0 + -5

Combine like terms: 0 + -5 = -5
5.666666667m + m2 = -5

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 = -5 + 8.027777782

Reorder the terms:
8.027777782 + 5.666666667m + m2 = -5 + 8.027777782

Combine like terms: -5 + 8.027777782 = 3.027777782
8.027777782 + 5.666666667m + m2 = 3.027777782

Factor a perfect square on the left side:
(m + 2.833333334)(m + 2.833333334) = 3.027777782

Calculate the square root of the right side: 1.740051086

Break this problem into two subproblems by setting 
(m + 2.833333334) equal to 1.740051086 and -1.740051086.


Subproblem 1
m + 2.833333334 = 1.740051086

Simplifying
m + 2.833333334 = 1.740051086

Reorder the terms:
2.833333334 + m = 1.740051086

Solving
2.833333334 + m = 1.740051086

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 = 1.740051086 + -2.833333334

Combine like terms: 2.833333334 + -2.833333334 = 0.000000000
0.000000000 + m = 1.740051086 + -2.833333334
m = 1.740051086 + -2.833333334

Combine like terms: 1.740051086 + -2.833333334 = -1.093282248
m = -1.093282248

Simplifying
m = -1.093282248


Subproblem 2
m + 2.833333334 = -1.740051086

Simplifying
m + 2.833333334 = -1.740051086

Reorder the terms:
2.833333334 + m = -1.740051086

Solving
2.833333334 + m = -1.740051086

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 = -1.740051086 + -2.833333334

Combine like terms: 2.833333334 + -2.833333334 = 0.000000000
0.000000000 + m = -1.740051086 + -2.833333334
m = -1.740051086 + -2.833333334

Combine like terms: -1.740051086 + -2.833333334 = -4.57338442
m = -4.57338442

Simplifying
m = -4.57338442


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {-1.093282248, -4.57338442}

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