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Simplifying -7m + 70 + -6(m + -1) = 9m(5m + -4) + -3m + 2 Reorder the terms: -7m + 70 + -6(-1 + m) = 9m(5m + -4) + -3m + 2 -7m + 70 + (-1 * -6 + m * -6) = 9m(5m + -4) + -3m + 2 -7m + 70 + (6 + -6m) = 9m(5m + -4) + -3m + 2 Reorder the terms: 70 + 6 + -7m + -6m = 9m(5m + -4) + -3m + 2 Combine like terms: 70 + 6 = 76 76 + -7m + -6m = 9m(5m + -4) + -3m + 2 Combine like terms: -7m + -6m = -13m 76 + -13m = 9m(5m + -4) + -3m + 2 Reorder the terms: 76 + -13m = 9m(-4 + 5m) + -3m + 2 76 + -13m = (-4 * 9m + 5m * 9m) + -3m + 2 76 + -13m = (-36m + 45m2) + -3m + 2 Reorder the terms: 76 + -13m = 2 + -36m + -3m + 45m2 Combine like terms: -36m + -3m = -39m 76 + -13m = 2 + -39m + 45m2 Solving 76 + -13m = 2 + -39m + 45m2 Solving for variable 'm'. Reorder the terms: 76 + -2 + -13m + 39m + -45m2 = 2 + -39m + 45m2 + -2 + 39m + -45m2 Combine like terms: 76 + -2 = 74 74 + -13m + 39m + -45m2 = 2 + -39m + 45m2 + -2 + 39m + -45m2 Combine like terms: -13m + 39m = 26m 74 + 26m + -45m2 = 2 + -39m + 45m2 + -2 + 39m + -45m2 Reorder the terms: 74 + 26m + -45m2 = 2 + -2 + -39m + 39m + 45m2 + -45m2 Combine like terms: 2 + -2 = 0 74 + 26m + -45m2 = 0 + -39m + 39m + 45m2 + -45m2 74 + 26m + -45m2 = -39m + 39m + 45m2 + -45m2 Combine like terms: -39m + 39m = 0 74 + 26m + -45m2 = 0 + 45m2 + -45m2 74 + 26m + -45m2 = 45m2 + -45m2 Combine like terms: 45m2 + -45m2 = 0 74 + 26m + -45m2 = 0 Begin completing the square. Divide all terms by -45 the coefficient of the squared term: Divide each side by '-45'. -1.644444444 + -0.5777777778m + m2 = 0 Move the constant term to the right: Add '1.644444444' to each side of the equation. -1.644444444 + -0.5777777778m + 1.644444444 + m2 = 0 + 1.644444444 Reorder the terms: -1.644444444 + 1.644444444 + -0.5777777778m + m2 = 0 + 1.644444444 Combine like terms: -1.644444444 + 1.644444444 = 0.000000000 0.000000000 + -0.5777777778m + m2 = 0 + 1.644444444 -0.5777777778m + m2 = 0 + 1.644444444 Combine like terms: 0 + 1.644444444 = 1.644444444 -0.5777777778m + m2 = 1.644444444 The m term is -0.5777777778m. Take half its coefficient (-0.2888888889). Square it (0.08345679013) and add it to both sides. Add '0.08345679013' to each side of the equation. -0.5777777778m + 0.08345679013 + m2 = 1.644444444 + 0.08345679013 Reorder the terms: 0.08345679013 + -0.5777777778m + m2 = 1.644444444 + 0.08345679013 Combine like terms: 1.644444444 + 0.08345679013 = 1.72790123413 0.08345679013 + -0.5777777778m + m2 = 1.72790123413 Factor a perfect square on the left side: (m + -0.2888888889)(m + -0.2888888889) = 1.72790123413 Calculate the square root of the right side: 1.314496571 Break this problem into two subproblems by setting (m + -0.2888888889) equal to 1.314496571 and -1.314496571.Subproblem 1
m + -0.2888888889 = 1.314496571 Simplifying m + -0.2888888889 = 1.314496571 Reorder the terms: -0.2888888889 + m = 1.314496571 Solving -0.2888888889 + m = 1.314496571 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.2888888889' to each side of the equation. -0.2888888889 + 0.2888888889 + m = 1.314496571 + 0.2888888889 Combine like terms: -0.2888888889 + 0.2888888889 = 0.0000000000 0.0000000000 + m = 1.314496571 + 0.2888888889 m = 1.314496571 + 0.2888888889 Combine like terms: 1.314496571 + 0.2888888889 = 1.6033854599 m = 1.6033854599 Simplifying m = 1.6033854599Subproblem 2
m + -0.2888888889 = -1.314496571 Simplifying m + -0.2888888889 = -1.314496571 Reorder the terms: -0.2888888889 + m = -1.314496571 Solving -0.2888888889 + m = -1.314496571 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.2888888889' to each side of the equation. -0.2888888889 + 0.2888888889 + m = -1.314496571 + 0.2888888889 Combine like terms: -0.2888888889 + 0.2888888889 = 0.0000000000 0.0000000000 + m = -1.314496571 + 0.2888888889 m = -1.314496571 + 0.2888888889 Combine like terms: -1.314496571 + 0.2888888889 = -1.0256076821 m = -1.0256076821 Simplifying m = -1.0256076821Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.6033854599, -1.0256076821}
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