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Simplifying 3m(2 + 4m) + -4(3 + -2m) = 0 (2 * 3m + 4m * 3m) + -4(3 + -2m) = 0 (6m + 12m2) + -4(3 + -2m) = 0 6m + 12m2 + (3 * -4 + -2m * -4) = 0 6m + 12m2 + (-12 + 8m) = 0 Reorder the terms: -12 + 6m + 8m + 12m2 = 0 Combine like terms: 6m + 8m = 14m -12 + 14m + 12m2 = 0 Solving -12 + 14m + 12m2 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), '2'. 2(-6 + 7m + 6m2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-6 + 7m + 6m2)' equal to zero and attempt to solve: Simplifying -6 + 7m + 6m2 = 0 Solving -6 + 7m + 6m2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -1 + 1.166666667m + m2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 1.166666667m + 1 + m2 = 0 + 1 Reorder the terms: -1 + 1 + 1.166666667m + m2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 1.166666667m + m2 = 0 + 1 1.166666667m + m2 = 0 + 1 Combine like terms: 0 + 1 = 1 1.166666667m + m2 = 1 The m term is 1.166666667m. Take half its coefficient (0.5833333335). Square it (0.3402777780) and add it to both sides. Add '0.3402777780' to each side of the equation. 1.166666667m + 0.3402777780 + m2 = 1 + 0.3402777780 Reorder the terms: 0.3402777780 + 1.166666667m + m2 = 1 + 0.3402777780 Combine like terms: 1 + 0.3402777780 = 1.340277778 0.3402777780 + 1.166666667m + m2 = 1.340277778 Factor a perfect square on the left side: (m + 0.5833333335)(m + 0.5833333335) = 1.340277778 Calculate the square root of the right side: 1.157703666 Break this problem into two subproblems by setting (m + 0.5833333335) equal to 1.157703666 and -1.157703666.Subproblem 1
m + 0.5833333335 = 1.157703666 Simplifying m + 0.5833333335 = 1.157703666 Reorder the terms: 0.5833333335 + m = 1.157703666 Solving 0.5833333335 + m = 1.157703666 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.5833333335' to each side of the equation. 0.5833333335 + -0.5833333335 + m = 1.157703666 + -0.5833333335 Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000 0.0000000000 + m = 1.157703666 + -0.5833333335 m = 1.157703666 + -0.5833333335 Combine like terms: 1.157703666 + -0.5833333335 = 0.5743703325 m = 0.5743703325 Simplifying m = 0.5743703325Subproblem 2
m + 0.5833333335 = -1.157703666 Simplifying m + 0.5833333335 = -1.157703666 Reorder the terms: 0.5833333335 + m = -1.157703666 Solving 0.5833333335 + m = -1.157703666 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.5833333335' to each side of the equation. 0.5833333335 + -0.5833333335 + m = -1.157703666 + -0.5833333335 Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000 0.0000000000 + m = -1.157703666 + -0.5833333335 m = -1.157703666 + -0.5833333335 Combine like terms: -1.157703666 + -0.5833333335 = -1.7410369995 m = -1.7410369995 Simplifying m = -1.7410369995Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.5743703325, -1.7410369995}Solution
m = {0.5743703325, -1.7410369995}
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