3m^2+29m=40

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Solution for 3m^2+29m=40 equation: 


Simplifying
3m2 + 29m = 40

Reorder the terms:
29m + 3m2 = 40

Solving
29m + 3m2 = 40

Solving for variable 'm'.

Reorder the terms:
-40 + 29m + 3m2 = 40 + -40

Combine like terms: 40 + -40 = 0
-40 + 29m + 3m2 = 0

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

Divide each side by '3'.
-13.33333333 + 9.666666667m + m2 = 0

Move the constant term to the right:

Add '13.33333333' to each side of the equation.
-13.33333333 + 9.666666667m + 13.33333333 + m2 = 0 + 13.33333333

Reorder the terms:
-13.33333333 + 13.33333333 + 9.666666667m + m2 = 0 + 13.33333333

Combine like terms: -13.33333333 + 13.33333333 = 0.00000000
0.00000000 + 9.666666667m + m2 = 0 + 13.33333333
9.666666667m + m2 = 0 + 13.33333333

Combine like terms: 0 + 13.33333333 = 13.33333333
9.666666667m + m2 = 13.33333333

The m term is 9.666666667m.  Take half its coefficient (4.833333334).
Square it (23.36111112) and add it to both sides.

Add '23.36111112' to each side of the equation.
9.666666667m + 23.36111112 + m2 = 13.33333333 + 23.36111112

Reorder the terms:
23.36111112 + 9.666666667m + m2 = 13.33333333 + 23.36111112

Combine like terms: 13.33333333 + 23.36111112 = 36.69444445
23.36111112 + 9.666666667m + m2 = 36.69444445

Factor a perfect square on the left side:
(m + 4.833333334)(m + 4.833333334) = 36.69444445

Calculate the square root of the right side: 6.057593949

Break this problem into two subproblems by setting 
(m + 4.833333334) equal to 6.057593949 and -6.057593949.


Subproblem 1
m + 4.833333334 = 6.057593949

Simplifying
m + 4.833333334 = 6.057593949

Reorder the terms:
4.833333334 + m = 6.057593949

Solving
4.833333334 + m = 6.057593949

Solving for variable 'm'.

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

Add '-4.833333334' to each side of the equation.
4.833333334 + -4.833333334 + m = 6.057593949 + -4.833333334

Combine like terms: 4.833333334 + -4.833333334 = 0.000000000
0.000000000 + m = 6.057593949 + -4.833333334
m = 6.057593949 + -4.833333334

Combine like terms: 6.057593949 + -4.833333334 = 1.224260615
m = 1.224260615

Simplifying
m = 1.224260615


Subproblem 2
m + 4.833333334 = -6.057593949

Simplifying
m + 4.833333334 = -6.057593949

Reorder the terms:
4.833333334 + m = -6.057593949

Solving
4.833333334 + m = -6.057593949

Solving for variable 'm'.

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

Add '-4.833333334' to each side of the equation.
4.833333334 + -4.833333334 + m = -6.057593949 + -4.833333334

Combine like terms: 4.833333334 + -4.833333334 = 0.000000000
0.000000000 + m = -6.057593949 + -4.833333334
m = -6.057593949 + -4.833333334

Combine like terms: -6.057593949 + -4.833333334 = -10.890927283
m = -10.890927283

Simplifying
m = -10.890927283


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {1.224260615, -10.890927283}

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