2m^2-12m=11

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Solution for 2m^2-12m=11 equation:


Simplifying
2m2 + -12m = 11

Reorder the terms:
-12m + 2m2 = 11

Solving
-12m + 2m2 = 11

Solving for variable 'm'.

Reorder the terms:
-11 + -12m + 2m2 = 11 + -11

Combine like terms: 11 + -11 = 0
-11 + -12m + 2m2 = 0

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

Divide each side by '2'.
-5.5 + -6m + m2 = 0

Move the constant term to the right:

Add '5.5' to each side of the equation.
-5.5 + -6m + 5.5 + m2 = 0 + 5.5

Reorder the terms:
-5.5 + 5.5 + -6m + m2 = 0 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + -6m + m2 = 0 + 5.5
-6m + m2 = 0 + 5.5

Combine like terms: 0 + 5.5 = 5.5
-6m + m2 = 5.5

The m term is -6m.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6m + 9 + m2 = 5.5 + 9

Reorder the terms:
9 + -6m + m2 = 5.5 + 9

Combine like terms: 5.5 + 9 = 14.5
9 + -6m + m2 = 14.5

Factor a perfect square on the left side:
(m + -3)(m + -3) = 14.5

Calculate the square root of the right side: 3.807886553

Break this problem into two subproblems by setting 
(m + -3) equal to 3.807886553 and -3.807886553.

Subproblem 1

m + -3 = 3.807886553 Simplifying m + -3 = 3.807886553 Reorder the terms: -3 + m = 3.807886553 Solving -3 + m = 3.807886553 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + m = 3.807886553 + 3 Combine like terms: -3 + 3 = 0 0 + m = 3.807886553 + 3 m = 3.807886553 + 3 Combine like terms: 3.807886553 + 3 = 6.807886553 m = 6.807886553 Simplifying m = 6.807886553

Subproblem 2

m + -3 = -3.807886553 Simplifying m + -3 = -3.807886553 Reorder the terms: -3 + m = -3.807886553 Solving -3 + m = -3.807886553 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + m = -3.807886553 + 3 Combine like terms: -3 + 3 = 0 0 + m = -3.807886553 + 3 m = -3.807886553 + 3 Combine like terms: -3.807886553 + 3 = -0.807886553 m = -0.807886553 Simplifying m = -0.807886553

Solution

The solution to the problem is based on the solutions from the subproblems. m = {6.807886553, -0.807886553}

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