4M^2+12+36M=0

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Solution for 4M^2+12+36M=0 equation: 


Simplifying
4M2 + 12 + 36M = 0

Reorder the terms:
12 + 36M + 4M2 = 0

Solving
12 + 36M + 4M2 = 0

Solving for variable 'M'.

Factor out the Greatest Common Factor (GCF), '4'.
4(3 + 9M + M2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(3 + 9M + M2)' equal to zero and attempt to solve:

Simplifying
3 + 9M + M2 = 0

Solving
3 + 9M + M2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + 9M + -3 + M2 = 0 + -3

Reorder the terms:
3 + -3 + 9M + M2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 9M + M2 = 0 + -3
9M + M2 = 0 + -3

Combine like terms: 0 + -3 = -3
9M + M2 = -3

The M term is 9M.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9M + 20.25 + M2 = -3 + 20.25

Reorder the terms:
20.25 + 9M + M2 = -3 + 20.25

Combine like terms: -3 + 20.25 = 17.25
20.25 + 9M + M2 = 17.25

Factor a perfect square on the left side:
(M + 4.5)(M + 4.5) = 17.25

Calculate the square root of the right side: 4.153311931

Break this problem into two subproblems by setting 
(M + 4.5) equal to 4.153311931 and -4.153311931.


Subproblem 1
M + 4.5 = 4.153311931

Simplifying
M + 4.5 = 4.153311931

Reorder the terms:
4.5 + M = 4.153311931

Solving
4.5 + M = 4.153311931

Solving for variable 'M'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + M = 4.153311931 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + M = 4.153311931 + -4.5
M = 4.153311931 + -4.5

Combine like terms: 4.153311931 + -4.5 = -0.346688069
M = -0.346688069

Simplifying
M = -0.346688069


Subproblem 2
M + 4.5 = -4.153311931

Simplifying
M + 4.5 = -4.153311931

Reorder the terms:
4.5 + M = -4.153311931

Solving
4.5 + M = -4.153311931

Solving for variable 'M'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + M = -4.153311931 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + M = -4.153311931 + -4.5
M = -4.153311931 + -4.5

Combine like terms: -4.153311931 + -4.5 = -8.653311931
M = -8.653311931

Simplifying
M = -8.653311931


Solution
The solution to the problem is based on the solutions
from the subproblems.
M = {-0.346688069, -8.653311931}
Solution
M = {-0.346688069, -8.653311931}

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