11-2m=-6(m-6)m

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Solution for 11-2m=-6(m-6)m equation:


Simplifying
11 + -2m = -6(m + -6) * m

Reorder the terms:
11 + -2m = -6(-6 + m) * m

Reorder the terms for easier multiplication:
11 + -2m = -6m(-6 + m)
11 + -2m = (-6 * -6m + m * -6m)
11 + -2m = (36m + -6m2)

Solving
11 + -2m = 36m + -6m2

Solving for variable 'm'.

Combine like terms: -2m + -36m = -38m
11 + -38m + 6m2 = 36m + -6m2 + -36m + 6m2

Reorder the terms:
11 + -38m + 6m2 = 36m + -36m + -6m2 + 6m2

Combine like terms: 36m + -36m = 0
11 + -38m + 6m2 = 0 + -6m2 + 6m2
11 + -38m + 6m2 = -6m2 + 6m2

Combine like terms: -6m2 + 6m2 = 0
11 + -38m + 6m2 = 0

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

Divide each side by '6'.
1.833333333 + -6.333333333m + m2 = 0

Move the constant term to the right:

Add '-1.833333333' to each side of the equation.
1.833333333 + -6.333333333m + -1.833333333 + m2 = 0 + -1.833333333

Reorder the terms:
1.833333333 + -1.833333333 + -6.333333333m + m2 = 0 + -1.833333333

Combine like terms: 1.833333333 + -1.833333333 = 0.000000000
0.000000000 + -6.333333333m + m2 = 0 + -1.833333333
-6.333333333m + m2 = 0 + -1.833333333

Combine like terms: 0 + -1.833333333 = -1.833333333
-6.333333333m + m2 = -1.833333333

The m term is -6.333333333m.  Take half its coefficient (-3.166666667).
Square it (10.02777778) and add it to both sides.

Add '10.02777778' to each side of the equation.
-6.333333333m + 10.02777778 + m2 = -1.833333333 + 10.02777778

Reorder the terms:
10.02777778 + -6.333333333m + m2 = -1.833333333 + 10.02777778

Combine like terms: -1.833333333 + 10.02777778 = 8.194444447
10.02777778 + -6.333333333m + m2 = 8.194444447

Factor a perfect square on the left side:
(m + -3.166666667)(m + -3.166666667) = 8.194444447

Calculate the square root of the right side: 2.862594007

Break this problem into two subproblems by setting 
(m + -3.166666667) equal to 2.862594007 and -2.862594007.

Subproblem 1

m + -3.166666667 = 2.862594007 Simplifying m + -3.166666667 = 2.862594007 Reorder the terms: -3.166666667 + m = 2.862594007 Solving -3.166666667 + m = 2.862594007 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '3.166666667' to each side of the equation. -3.166666667 + 3.166666667 + m = 2.862594007 + 3.166666667 Combine like terms: -3.166666667 + 3.166666667 = 0.000000000 0.000000000 + m = 2.862594007 + 3.166666667 m = 2.862594007 + 3.166666667 Combine like terms: 2.862594007 + 3.166666667 = 6.029260674 m = 6.029260674 Simplifying m = 6.029260674

Subproblem 2

m + -3.166666667 = -2.862594007 Simplifying m + -3.166666667 = -2.862594007 Reorder the terms: -3.166666667 + m = -2.862594007 Solving -3.166666667 + m = -2.862594007 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '3.166666667' to each side of the equation. -3.166666667 + 3.166666667 + m = -2.862594007 + 3.166666667 Combine like terms: -3.166666667 + 3.166666667 = 0.000000000 0.000000000 + m = -2.862594007 + 3.166666667 m = -2.862594007 + 3.166666667 Combine like terms: -2.862594007 + 3.166666667 = 0.30407266 m = 0.30407266 Simplifying m = 0.30407266

Solution

The solution to the problem is based on the solutions from the subproblems. m = {6.029260674, 0.30407266}

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