(3m^2-11m-2)=

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Solution for (3m^2-11m-2)= equation:


Simplifying
(3m2 + -11m + -2) = 0

Reorder the terms:
(-2 + -11m + 3m2) = 0

Remove parenthesis around (-2 + -11m + 3m2)
-2 + -11m + 3m2 = 0

Solving
-2 + -11m + 3m2 = 0

Solving for variable 'm'.

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

Divide each side by '3'.
-0.6666666667 + -3.666666667m + m2 = 0

Move the constant term to the right:

Add '0.6666666667' to each side of the equation.
-0.6666666667 + -3.666666667m + 0.6666666667 + m2 = 0 + 0.6666666667

Reorder the terms:
-0.6666666667 + 0.6666666667 + -3.666666667m + m2 = 0 + 0.6666666667

Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000
0.0000000000 + -3.666666667m + m2 = 0 + 0.6666666667
-3.666666667m + m2 = 0 + 0.6666666667

Combine like terms: 0 + 0.6666666667 = 0.6666666667
-3.666666667m + m2 = 0.6666666667

The m term is -3.666666667m.  Take half its coefficient (-1.833333334).
Square it (3.361111114) and add it to both sides.

Add '3.361111114' to each side of the equation.
-3.666666667m + 3.361111114 + m2 = 0.6666666667 + 3.361111114

Reorder the terms:
3.361111114 + -3.666666667m + m2 = 0.6666666667 + 3.361111114

Combine like terms: 0.6666666667 + 3.361111114 = 4.0277777807
3.361111114 + -3.666666667m + m2 = 4.0277777807

Factor a perfect square on the left side:
(m + -1.833333334)(m + -1.833333334) = 4.0277777807

Calculate the square root of the right side: 2.006932431

Break this problem into two subproblems by setting 
(m + -1.833333334) equal to 2.006932431 and -2.006932431.

Subproblem 1

m + -1.833333334 = 2.006932431 Simplifying m + -1.833333334 = 2.006932431 Reorder the terms: -1.833333334 + m = 2.006932431 Solving -1.833333334 + m = 2.006932431 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1.833333334' to each side of the equation. -1.833333334 + 1.833333334 + m = 2.006932431 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + m = 2.006932431 + 1.833333334 m = 2.006932431 + 1.833333334 Combine like terms: 2.006932431 + 1.833333334 = 3.840265765 m = 3.840265765 Simplifying m = 3.840265765

Subproblem 2

m + -1.833333334 = -2.006932431 Simplifying m + -1.833333334 = -2.006932431 Reorder the terms: -1.833333334 + m = -2.006932431 Solving -1.833333334 + m = -2.006932431 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1.833333334' to each side of the equation. -1.833333334 + 1.833333334 + m = -2.006932431 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + m = -2.006932431 + 1.833333334 m = -2.006932431 + 1.833333334 Combine like terms: -2.006932431 + 1.833333334 = -0.173599097 m = -0.173599097 Simplifying m = -0.173599097

Solution

The solution to the problem is based on the solutions from the subproblems. m = {3.840265765, -0.173599097}

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