12m^2+11m-18=0

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Solution for 12m^2+11m-18=0 equation:


Simplifying
12m2 + 11m + -18 = 0

Reorder the terms:
-18 + 11m + 12m2 = 0

Solving
-18 + 11m + 12m2 = 0

Solving for variable 'm'.

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

Divide each side by '12'.
-1.5 + 0.9166666667m + m2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + 0.9166666667m + 1.5 + m2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + 0.9166666667m + m2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + 0.9166666667m + m2 = 0 + 1.5
0.9166666667m + m2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
0.9166666667m + m2 = 1.5

The m term is 0.9166666667m.  Take half its coefficient (0.4583333334).
Square it (0.2100694445) and add it to both sides.

Add '0.2100694445' to each side of the equation.
0.9166666667m + 0.2100694445 + m2 = 1.5 + 0.2100694445

Reorder the terms:
0.2100694445 + 0.9166666667m + m2 = 1.5 + 0.2100694445

Combine like terms: 1.5 + 0.2100694445 = 1.7100694445
0.2100694445 + 0.9166666667m + m2 = 1.7100694445

Factor a perfect square on the left side:
(m + 0.4583333334)(m + 0.4583333334) = 1.7100694445

Calculate the square root of the right side: 1.307696236

Break this problem into two subproblems by setting 
(m + 0.4583333334) equal to 1.307696236 and -1.307696236.

Subproblem 1

m + 0.4583333334 = 1.307696236 Simplifying m + 0.4583333334 = 1.307696236 Reorder the terms: 0.4583333334 + m = 1.307696236 Solving 0.4583333334 + m = 1.307696236 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.4583333334' to each side of the equation. 0.4583333334 + -0.4583333334 + m = 1.307696236 + -0.4583333334 Combine like terms: 0.4583333334 + -0.4583333334 = 0.0000000000 0.0000000000 + m = 1.307696236 + -0.4583333334 m = 1.307696236 + -0.4583333334 Combine like terms: 1.307696236 + -0.4583333334 = 0.8493629026 m = 0.8493629026 Simplifying m = 0.8493629026

Subproblem 2

m + 0.4583333334 = -1.307696236 Simplifying m + 0.4583333334 = -1.307696236 Reorder the terms: 0.4583333334 + m = -1.307696236 Solving 0.4583333334 + m = -1.307696236 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.4583333334' to each side of the equation. 0.4583333334 + -0.4583333334 + m = -1.307696236 + -0.4583333334 Combine like terms: 0.4583333334 + -0.4583333334 = 0.0000000000 0.0000000000 + m = -1.307696236 + -0.4583333334 m = -1.307696236 + -0.4583333334 Combine like terms: -1.307696236 + -0.4583333334 = -1.7660295694 m = -1.7660295694 Simplifying m = -1.7660295694

Solution

The solution to the problem is based on the solutions from the subproblems. m = {0.8493629026, -1.7660295694}

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