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Simplifying 15m2 = 82m + 24 Reorder the terms: 15m2 = 24 + 82m Solving 15m2 = 24 + 82m Solving for variable 'm'. Reorder the terms: -24 + -82m + 15m2 = 24 + 82m + -24 + -82m Reorder the terms: -24 + -82m + 15m2 = 24 + -24 + 82m + -82m Combine like terms: 24 + -24 = 0 -24 + -82m + 15m2 = 0 + 82m + -82m -24 + -82m + 15m2 = 82m + -82m Combine like terms: 82m + -82m = 0 -24 + -82m + 15m2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -1.6 + -5.466666667m + m2 = 0 Move the constant term to the right: Add '1.6' to each side of the equation. -1.6 + -5.466666667m + 1.6 + m2 = 0 + 1.6 Reorder the terms: -1.6 + 1.6 + -5.466666667m + m2 = 0 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + -5.466666667m + m2 = 0 + 1.6 -5.466666667m + m2 = 0 + 1.6 Combine like terms: 0 + 1.6 = 1.6 -5.466666667m + m2 = 1.6 The m term is -5.466666667m. Take half its coefficient (-2.733333334). Square it (7.471111115) and add it to both sides. Add '7.471111115' to each side of the equation. -5.466666667m + 7.471111115 + m2 = 1.6 + 7.471111115 Reorder the terms: 7.471111115 + -5.466666667m + m2 = 1.6 + 7.471111115 Combine like terms: 1.6 + 7.471111115 = 9.071111115 7.471111115 + -5.466666667m + m2 = 9.071111115 Factor a perfect square on the left side: (m + -2.733333334)(m + -2.733333334) = 9.071111115 Calculate the square root of the right side: 3.011828533 Break this problem into two subproblems by setting (m + -2.733333334) equal to 3.011828533 and -3.011828533.Subproblem 1
m + -2.733333334 = 3.011828533 Simplifying m + -2.733333334 = 3.011828533 Reorder the terms: -2.733333334 + m = 3.011828533 Solving -2.733333334 + m = 3.011828533 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '2.733333334' to each side of the equation. -2.733333334 + 2.733333334 + m = 3.011828533 + 2.733333334 Combine like terms: -2.733333334 + 2.733333334 = 0.000000000 0.000000000 + m = 3.011828533 + 2.733333334 m = 3.011828533 + 2.733333334 Combine like terms: 3.011828533 + 2.733333334 = 5.745161867 m = 5.745161867 Simplifying m = 5.745161867Subproblem 2
m + -2.733333334 = -3.011828533 Simplifying m + -2.733333334 = -3.011828533 Reorder the terms: -2.733333334 + m = -3.011828533 Solving -2.733333334 + m = -3.011828533 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '2.733333334' to each side of the equation. -2.733333334 + 2.733333334 + m = -3.011828533 + 2.733333334 Combine like terms: -2.733333334 + 2.733333334 = 0.000000000 0.000000000 + m = -3.011828533 + 2.733333334 m = -3.011828533 + 2.733333334 Combine like terms: -3.011828533 + 2.733333334 = -0.278495199 m = -0.278495199 Simplifying m = -0.278495199Solution
The solution to the problem is based on the solutions from the subproblems. m = {5.745161867, -0.278495199}
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