M^2+3M-30=0

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Solution for M^2+3M-30=0 equation: 


Simplifying
M2 + 3M + -30 = 0

Reorder the terms:
-30 + 3M + M2 = 0

Solving
-30 + 3M + M2 = 0

Solving for variable 'M'.

Begin completing the square.

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + 3M + 30 + M2 = 0 + 30

Reorder the terms:
-30 + 30 + 3M + M2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + 3M + M2 = 0 + 30
3M + M2 = 0 + 30

Combine like terms: 0 + 30 = 30
3M + M2 = 30

The M term is 3M.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3M + 2.25 + M2 = 30 + 2.25

Reorder the terms:
2.25 + 3M + M2 = 30 + 2.25

Combine like terms: 30 + 2.25 = 32.25
2.25 + 3M + M2 = 32.25

Factor a perfect square on the left side:
(M + 1.5)(M + 1.5) = 32.25

Calculate the square root of the right side: 5.678908346

Break this problem into two subproblems by setting 
(M + 1.5) equal to 5.678908346 and -5.678908346.


Subproblem 1
M + 1.5 = 5.678908346

Simplifying
M + 1.5 = 5.678908346

Reorder the terms:
1.5 + M = 5.678908346

Solving
1.5 + M = 5.678908346

Solving for variable 'M'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + M = 5.678908346 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + M = 5.678908346 + -1.5
M = 5.678908346 + -1.5

Combine like terms: 5.678908346 + -1.5 = 4.178908346
M = 4.178908346

Simplifying
M = 4.178908346


Subproblem 2
M + 1.5 = -5.678908346

Simplifying
M + 1.5 = -5.678908346

Reorder the terms:
1.5 + M = -5.678908346

Solving
1.5 + M = -5.678908346

Solving for variable 'M'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + M = -5.678908346 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + M = -5.678908346 + -1.5
M = -5.678908346 + -1.5

Combine like terms: -5.678908346 + -1.5 = -7.178908346
M = -7.178908346

Simplifying
M = -7.178908346


Solution
The solution to the problem is based on the solutions
from the subproblems.
M = {4.178908346, -7.178908346}

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