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Simplifying -4m(3m + 5) = -29m + -20 Reorder the terms: -4m(5 + 3m) = -29m + -20 (5 * -4m + 3m * -4m) = -29m + -20 (-20m + -12m2) = -29m + -20 Reorder the terms: -20m + -12m2 = -20 + -29m Solving -20m + -12m2 = -20 + -29m Solving for variable 'm'. Reorder the terms: 20 + -20m + 29m + -12m2 = -20 + -29m + 20 + 29m Combine like terms: -20m + 29m = 9m 20 + 9m + -12m2 = -20 + -29m + 20 + 29m Reorder the terms: 20 + 9m + -12m2 = -20 + 20 + -29m + 29m Combine like terms: -20 + 20 = 0 20 + 9m + -12m2 = 0 + -29m + 29m 20 + 9m + -12m2 = -29m + 29m Combine like terms: -29m + 29m = 0 20 + 9m + -12m2 = 0 Begin completing the square. Divide all terms by -12 the coefficient of the squared term: Divide each side by '-12'. -1.666666667 + -0.75m + m2 = 0 Move the constant term to the right: Add '1.666666667' to each side of the equation. -1.666666667 + -0.75m + 1.666666667 + m2 = 0 + 1.666666667 Reorder the terms: -1.666666667 + 1.666666667 + -0.75m + m2 = 0 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + -0.75m + m2 = 0 + 1.666666667 -0.75m + m2 = 0 + 1.666666667 Combine like terms: 0 + 1.666666667 = 1.666666667 -0.75m + m2 = 1.666666667 The m term is -0.75m. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75m + 0.140625 + m2 = 1.666666667 + 0.140625 Reorder the terms: 0.140625 + -0.75m + m2 = 1.666666667 + 0.140625 Combine like terms: 1.666666667 + 0.140625 = 1.807291667 0.140625 + -0.75m + m2 = 1.807291667 Factor a perfect square on the left side: (m + -0.375)(m + -0.375) = 1.807291667 Calculate the square root of the right side: 1.344355484 Break this problem into two subproblems by setting (m + -0.375) equal to 1.344355484 and -1.344355484.Subproblem 1
m + -0.375 = 1.344355484 Simplifying m + -0.375 = 1.344355484 Reorder the terms: -0.375 + m = 1.344355484 Solving -0.375 + m = 1.344355484 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + m = 1.344355484 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + m = 1.344355484 + 0.375 m = 1.344355484 + 0.375 Combine like terms: 1.344355484 + 0.375 = 1.719355484 m = 1.719355484 Simplifying m = 1.719355484Subproblem 2
m + -0.375 = -1.344355484 Simplifying m + -0.375 = -1.344355484 Reorder the terms: -0.375 + m = -1.344355484 Solving -0.375 + m = -1.344355484 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + m = -1.344355484 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + m = -1.344355484 + 0.375 m = -1.344355484 + 0.375 Combine like terms: -1.344355484 + 0.375 = -0.969355484 m = -0.969355484 Simplifying m = -0.969355484Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.719355484, -0.969355484}
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