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Simplifying 3m(8 + -3m) = -16 (8 * 3m + -3m * 3m) = -16 (24m + -9m2) = -16 Solving 24m + -9m2 = -16 Solving for variable 'm'. Reorder the terms: 16 + 24m + -9m2 = -16 + 16 Combine like terms: -16 + 16 = 0 16 + 24m + -9m2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -1.777777778 + -2.666666667m + m2 = 0 Move the constant term to the right: Add '1.777777778' to each side of the equation. -1.777777778 + -2.666666667m + 1.777777778 + m2 = 0 + 1.777777778 Reorder the terms: -1.777777778 + 1.777777778 + -2.666666667m + m2 = 0 + 1.777777778 Combine like terms: -1.777777778 + 1.777777778 = 0.000000000 0.000000000 + -2.666666667m + m2 = 0 + 1.777777778 -2.666666667m + m2 = 0 + 1.777777778 Combine like terms: 0 + 1.777777778 = 1.777777778 -2.666666667m + m2 = 1.777777778 The m term is -2.666666667m. Take half its coefficient (-1.333333334). Square it (1.777777780) and add it to both sides. Add '1.777777780' to each side of the equation. -2.666666667m + 1.777777780 + m2 = 1.777777778 + 1.777777780 Reorder the terms: 1.777777780 + -2.666666667m + m2 = 1.777777778 + 1.777777780 Combine like terms: 1.777777778 + 1.777777780 = 3.555555558 1.777777780 + -2.666666667m + m2 = 3.555555558 Factor a perfect square on the left side: (m + -1.333333334)(m + -1.333333334) = 3.555555558 Calculate the square root of the right side: 1.885618084 Break this problem into two subproblems by setting (m + -1.333333334) equal to 1.885618084 and -1.885618084.Subproblem 1
m + -1.333333334 = 1.885618084 Simplifying m + -1.333333334 = 1.885618084 Reorder the terms: -1.333333334 + m = 1.885618084 Solving -1.333333334 + m = 1.885618084 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1.333333334' to each side of the equation. -1.333333334 + 1.333333334 + m = 1.885618084 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + m = 1.885618084 + 1.333333334 m = 1.885618084 + 1.333333334 Combine like terms: 1.885618084 + 1.333333334 = 3.218951418 m = 3.218951418 Simplifying m = 3.218951418Subproblem 2
m + -1.333333334 = -1.885618084 Simplifying m + -1.333333334 = -1.885618084 Reorder the terms: -1.333333334 + m = -1.885618084 Solving -1.333333334 + m = -1.885618084 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1.333333334' to each side of the equation. -1.333333334 + 1.333333334 + m = -1.885618084 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + m = -1.885618084 + 1.333333334 m = -1.885618084 + 1.333333334 Combine like terms: -1.885618084 + 1.333333334 = -0.55228475 m = -0.55228475 Simplifying m = -0.55228475Solution
The solution to the problem is based on the solutions from the subproblems. m = {3.218951418, -0.55228475}
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