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Simplifying 12m3 + -5m2 + -12m = 0 Reorder the terms: -12m + -5m2 + 12m3 = 0 Solving -12m + -5m2 + 12m3 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), 'm'. m(-12 + -5m + 12m2) = 0Subproblem 1
Set the factor 'm' equal to zero and attempt to solve: Simplifying m = 0 Solving m = 0 Move all terms containing m to the left, all other terms to the right. Simplifying m = 0Subproblem 2
Set the factor '(-12 + -5m + 12m2)' equal to zero and attempt to solve: Simplifying -12 + -5m + 12m2 = 0 Solving -12 + -5m + 12m2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -1 + -0.4166666667m + m2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -0.4166666667m + 1 + m2 = 0 + 1 Reorder the terms: -1 + 1 + -0.4166666667m + m2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -0.4166666667m + m2 = 0 + 1 -0.4166666667m + m2 = 0 + 1 Combine like terms: 0 + 1 = 1 -0.4166666667m + m2 = 1 The m term is -0.4166666667m. Take half its coefficient (-0.2083333334). Square it (0.04340277781) and add it to both sides. Add '0.04340277781' to each side of the equation. -0.4166666667m + 0.04340277781 + m2 = 1 + 0.04340277781 Reorder the terms: 0.04340277781 + -0.4166666667m + m2 = 1 + 0.04340277781 Combine like terms: 1 + 0.04340277781 = 1.04340277781 0.04340277781 + -0.4166666667m + m2 = 1.04340277781 Factor a perfect square on the left side: (m + -0.2083333334)(m + -0.2083333334) = 1.04340277781 Calculate the square root of the right side: 1.021470889 Break this problem into two subproblems by setting (m + -0.2083333334) equal to 1.021470889 and -1.021470889.Subproblem 1
m + -0.2083333334 = 1.021470889 Simplifying m + -0.2083333334 = 1.021470889 Reorder the terms: -0.2083333334 + m = 1.021470889 Solving -0.2083333334 + m = 1.021470889 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.2083333334' to each side of the equation. -0.2083333334 + 0.2083333334 + m = 1.021470889 + 0.2083333334 Combine like terms: -0.2083333334 + 0.2083333334 = 0.0000000000 0.0000000000 + m = 1.021470889 + 0.2083333334 m = 1.021470889 + 0.2083333334 Combine like terms: 1.021470889 + 0.2083333334 = 1.2298042224 m = 1.2298042224 Simplifying m = 1.2298042224Subproblem 2
m + -0.2083333334 = -1.021470889 Simplifying m + -0.2083333334 = -1.021470889 Reorder the terms: -0.2083333334 + m = -1.021470889 Solving -0.2083333334 + m = -1.021470889 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.2083333334' to each side of the equation. -0.2083333334 + 0.2083333334 + m = -1.021470889 + 0.2083333334 Combine like terms: -0.2083333334 + 0.2083333334 = 0.0000000000 0.0000000000 + m = -1.021470889 + 0.2083333334 m = -1.021470889 + 0.2083333334 Combine like terms: -1.021470889 + 0.2083333334 = -0.8131375556 m = -0.8131375556 Simplifying m = -0.8131375556Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.2298042224, -0.8131375556}Solution
m = {0, 1.2298042224, -0.8131375556}
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