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Simplifying (7m2 + 3m + -4) + -1(3m2 + 9 + -5) = 0 Reorder the terms: (-4 + 3m + 7m2) + -1(3m2 + 9 + -5) = 0 Remove parenthesis around (-4 + 3m + 7m2) -4 + 3m + 7m2 + -1(3m2 + 9 + -5) = 0 Reorder the terms: -4 + 3m + 7m2 + -1(9 + -5 + 3m2) = 0 Combine like terms: 9 + -5 = 4 -4 + 3m + 7m2 + -1(4 + 3m2) = 0 -4 + 3m + 7m2 + (4 * -1 + 3m2 * -1) = 0 -4 + 3m + 7m2 + (-4 + -3m2) = 0 Reorder the terms: -4 + -4 + 3m + 7m2 + -3m2 = 0 Combine like terms: -4 + -4 = -8 -8 + 3m + 7m2 + -3m2 = 0 Combine like terms: 7m2 + -3m2 = 4m2 -8 + 3m + 4m2 = 0 Solving -8 + 3m + 4m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2 + 0.75m + m2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 0.75m + 2 + m2 = 0 + 2 Reorder the terms: -2 + 2 + 0.75m + m2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 0.75m + m2 = 0 + 2 0.75m + m2 = 0 + 2 Combine like terms: 0 + 2 = 2 0.75m + m2 = 2 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 = 2 + 0.140625 Reorder the terms: 0.140625 + 0.75m + m2 = 2 + 0.140625 Combine like terms: 2 + 0.140625 = 2.140625 0.140625 + 0.75m + m2 = 2.140625 Factor a perfect square on the left side: (m + 0.375)(m + 0.375) = 2.140625 Calculate the square root of the right side: 1.463087489 Break this problem into two subproblems by setting (m + 0.375) equal to 1.463087489 and -1.463087489.Subproblem 1
m + 0.375 = 1.463087489 Simplifying m + 0.375 = 1.463087489 Reorder the terms: 0.375 + m = 1.463087489 Solving 0.375 + m = 1.463087489 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 = 1.463087489 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + m = 1.463087489 + -0.375 m = 1.463087489 + -0.375 Combine like terms: 1.463087489 + -0.375 = 1.088087489 m = 1.088087489 Simplifying m = 1.088087489Subproblem 2
m + 0.375 = -1.463087489 Simplifying m + 0.375 = -1.463087489 Reorder the terms: 0.375 + m = -1.463087489 Solving 0.375 + m = -1.463087489 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 = -1.463087489 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + m = -1.463087489 + -0.375 m = -1.463087489 + -0.375 Combine like terms: -1.463087489 + -0.375 = -1.838087489 m = -1.838087489 Simplifying m = -1.838087489Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.088087489, -1.838087489}
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