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Simplifying 15m2 + 31m + 2 = 8 Reorder the terms: 2 + 31m + 15m2 = 8 Solving 2 + 31m + 15m2 = 8 Solving for variable 'm'. Reorder the terms: 2 + -8 + 31m + 15m2 = 8 + -8 Combine like terms: 2 + -8 = -6 -6 + 31m + 15m2 = 8 + -8 Combine like terms: 8 + -8 = 0 -6 + 31m + 15m2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -0.4 + 2.066666667m + m2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + 2.066666667m + 0.4 + m2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + 2.066666667m + m2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + 2.066666667m + m2 = 0 + 0.4 2.066666667m + m2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 2.066666667m + m2 = 0.4 The m term is 2.066666667m. Take half its coefficient (1.033333334). Square it (1.067777779) and add it to both sides. Add '1.067777779' to each side of the equation. 2.066666667m + 1.067777779 + m2 = 0.4 + 1.067777779 Reorder the terms: 1.067777779 + 2.066666667m + m2 = 0.4 + 1.067777779 Combine like terms: 0.4 + 1.067777779 = 1.467777779 1.067777779 + 2.066666667m + m2 = 1.467777779 Factor a perfect square on the left side: (m + 1.033333334)(m + 1.033333334) = 1.467777779 Calculate the square root of the right side: 1.21151879 Break this problem into two subproblems by setting (m + 1.033333334) equal to 1.21151879 and -1.21151879.Subproblem 1
m + 1.033333334 = 1.21151879 Simplifying m + 1.033333334 = 1.21151879 Reorder the terms: 1.033333334 + m = 1.21151879 Solving 1.033333334 + m = 1.21151879 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1.033333334' to each side of the equation. 1.033333334 + -1.033333334 + m = 1.21151879 + -1.033333334 Combine like terms: 1.033333334 + -1.033333334 = 0.000000000 0.000000000 + m = 1.21151879 + -1.033333334 m = 1.21151879 + -1.033333334 Combine like terms: 1.21151879 + -1.033333334 = 0.178185456 m = 0.178185456 Simplifying m = 0.178185456Subproblem 2
m + 1.033333334 = -1.21151879 Simplifying m + 1.033333334 = -1.21151879 Reorder the terms: 1.033333334 + m = -1.21151879 Solving 1.033333334 + m = -1.21151879 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1.033333334' to each side of the equation. 1.033333334 + -1.033333334 + m = -1.21151879 + -1.033333334 Combine like terms: 1.033333334 + -1.033333334 = 0.000000000 0.000000000 + m = -1.21151879 + -1.033333334 m = -1.21151879 + -1.033333334 Combine like terms: -1.21151879 + -1.033333334 = -2.244852124 m = -2.244852124 Simplifying m = -2.244852124Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.178185456, -2.244852124}
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