-2M(M-23)-6=60

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Solution for -2M(M-23)-6=60 equation: 


Simplifying
-2M(M + -23) + -6 = 60

Reorder the terms:
-2M(-23 + M) + -6 = 60
(-23 * -2M + M * -2M) + -6 = 60
(46M + -2M2) + -6 = 60

Reorder the terms:
-6 + 46M + -2M2 = 60

Solving
-6 + 46M + -2M2 = 60

Solving for variable 'M'.

Reorder the terms:
-6 + -60 + 46M + -2M2 = 60 + -60

Combine like terms: -6 + -60 = -66
-66 + 46M + -2M2 = 60 + -60

Combine like terms: 60 + -60 = 0
-66 + 46M + -2M2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-33 + 23M + -1M2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-33 + 23M + -1M2)' equal to zero and attempt to solve:

Simplifying
-33 + 23M + -1M2 = 0

Solving
-33 + 23M + -1M2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
33 + -23M + M2 = 0

Move the constant term to the right:

Add '-33' to each side of the equation.
33 + -23M + -33 + M2 = 0 + -33

Reorder the terms:
33 + -33 + -23M + M2 = 0 + -33

Combine like terms: 33 + -33 = 0
0 + -23M + M2 = 0 + -33
-23M + M2 = 0 + -33

Combine like terms: 0 + -33 = -33
-23M + M2 = -33

The M term is -23M.  Take half its coefficient (-11.5).
Square it (132.25) and add it to both sides.

Add '132.25' to each side of the equation.
-23M + 132.25 + M2 = -33 + 132.25

Reorder the terms:
132.25 + -23M + M2 = -33 + 132.25

Combine like terms: -33 + 132.25 = 99.25
132.25 + -23M + M2 = 99.25

Factor a perfect square on the left side:
(M + -11.5)(M + -11.5) = 99.25

Calculate the square root of the right side: 9.962429423

Break this problem into two subproblems by setting 
(M + -11.5) equal to 9.962429423 and -9.962429423.


Subproblem 1
M + -11.5 = 9.962429423

Simplifying
M + -11.5 = 9.962429423

Reorder the terms:
-11.5 + M = 9.962429423

Solving
-11.5 + M = 9.962429423

Solving for variable 'M'.

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

Add '11.5' to each side of the equation.
-11.5 + 11.5 + M = 9.962429423 + 11.5

Combine like terms: -11.5 + 11.5 = 0.0
0.0 + M = 9.962429423 + 11.5
M = 9.962429423 + 11.5

Combine like terms: 9.962429423 + 11.5 = 21.462429423
M = 21.462429423

Simplifying
M = 21.462429423


Subproblem 2
M + -11.5 = -9.962429423

Simplifying
M + -11.5 = -9.962429423

Reorder the terms:
-11.5 + M = -9.962429423

Solving
-11.5 + M = -9.962429423

Solving for variable 'M'.

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

Add '11.5' to each side of the equation.
-11.5 + 11.5 + M = -9.962429423 + 11.5

Combine like terms: -11.5 + 11.5 = 0.0
0.0 + M = -9.962429423 + 11.5
M = -9.962429423 + 11.5

Combine like terms: -9.962429423 + 11.5 = 1.537570577
M = 1.537570577

Simplifying
M = 1.537570577


Solution
The solution to the problem is based on the solutions
from the subproblems.
M = {21.462429423, 1.537570577}
Solution
M = {21.462429423, 1.537570577}

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