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Simplifying (3 + -7m) + 2(3.5m + 1)(3 + -7m) + 2(3.5m + 1) = 0 Remove parenthesis around (3 + -7m) 3 + -7m + 2(3.5m + 1)(3 + -7m) + 2(3.5m + 1) = 0 Reorder the terms: 3 + -7m + 2(1 + 3.5m)(3 + -7m) + 2(3.5m + 1) = 0 Multiply (1 + 3.5m) * (3 + -7m) 3 + -7m + 2(1(3 + -7m) + 3.5m * (3 + -7m)) + 2(3.5m + 1) = 0 3 + -7m + 2((3 * 1 + -7m * 1) + 3.5m * (3 + -7m)) + 2(3.5m + 1) = 0 3 + -7m + 2((3 + -7m) + 3.5m * (3 + -7m)) + 2(3.5m + 1) = 0 3 + -7m + 2(3 + -7m + (3 * 3.5m + -7m * 3.5m)) + 2(3.5m + 1) = 0 3 + -7m + 2(3 + -7m + (10.5m + -24.5m2)) + 2(3.5m + 1) = 0 Combine like terms: -7m + 10.5m = 3.5m 3 + -7m + 2(3 + 3.5m + -24.5m2) + 2(3.5m + 1) = 0 3 + -7m + (3 * 2 + 3.5m * 2 + -24.5m2 * 2) + 2(3.5m + 1) = 0 3 + -7m + (6 + 7m + -49m2) + 2(3.5m + 1) = 0 Reorder the terms: 3 + -7m + 6 + 7m + -49m2 + 2(1 + 3.5m) = 0 3 + -7m + 6 + 7m + -49m2 + (1 * 2 + 3.5m * 2) = 0 3 + -7m + 6 + 7m + -49m2 + (2 + 7m) = 0 Reorder the terms: 3 + 6 + 2 + -7m + 7m + 7m + -49m2 = 0 Combine like terms: 3 + 6 = 9 9 + 2 + -7m + 7m + 7m + -49m2 = 0 Combine like terms: 9 + 2 = 11 11 + -7m + 7m + 7m + -49m2 = 0 Combine like terms: -7m + 7m = 0 11 + 0 + 7m + -49m2 = 0 11 + 7m + -49m2 = 0 Solving 11 + 7m + -49m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by -49 the coefficient of the squared term: Divide each side by '-49'. -0.2244897959 + -0.1428571429m + m2 = 0 Move the constant term to the right: Add '0.2244897959' to each side of the equation. -0.2244897959 + -0.1428571429m + 0.2244897959 + m2 = 0 + 0.2244897959 Reorder the terms: -0.2244897959 + 0.2244897959 + -0.1428571429m + m2 = 0 + 0.2244897959 Combine like terms: -0.2244897959 + 0.2244897959 = 0.0000000000 0.0000000000 + -0.1428571429m + m2 = 0 + 0.2244897959 -0.1428571429m + m2 = 0 + 0.2244897959 Combine like terms: 0 + 0.2244897959 = 0.2244897959 -0.1428571429m + m2 = 0.2244897959 The m term is -0.1428571429m. Take half its coefficient (-0.07142857145). Square it (0.005102040819) and add it to both sides. Add '0.005102040819' to each side of the equation. -0.1428571429m + 0.005102040819 + m2 = 0.2244897959 + 0.005102040819 Reorder the terms: 0.005102040819 + -0.1428571429m + m2 = 0.2244897959 + 0.005102040819 Combine like terms: 0.2244897959 + 0.005102040819 = 0.229591836719 0.005102040819 + -0.1428571429m + m2 = 0.229591836719 Factor a perfect square on the left side: (m + -0.07142857145)(m + -0.07142857145) = 0.229591836719 Calculate the square root of the right side: 0.479157424 Break this problem into two subproblems by setting (m + -0.07142857145) equal to 0.479157424 and -0.479157424.Subproblem 1
m + -0.07142857145 = 0.479157424 Simplifying m + -0.07142857145 = 0.479157424 Reorder the terms: -0.07142857145 + m = 0.479157424 Solving -0.07142857145 + m = 0.479157424 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.07142857145' to each side of the equation. -0.07142857145 + 0.07142857145 + m = 0.479157424 + 0.07142857145 Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000 0.00000000000 + m = 0.479157424 + 0.07142857145 m = 0.479157424 + 0.07142857145 Combine like terms: 0.479157424 + 0.07142857145 = 0.55058599545 m = 0.55058599545 Simplifying m = 0.55058599545Subproblem 2
m + -0.07142857145 = -0.479157424 Simplifying m + -0.07142857145 = -0.479157424 Reorder the terms: -0.07142857145 + m = -0.479157424 Solving -0.07142857145 + m = -0.479157424 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.07142857145' to each side of the equation. -0.07142857145 + 0.07142857145 + m = -0.479157424 + 0.07142857145 Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000 0.00000000000 + m = -0.479157424 + 0.07142857145 m = -0.479157424 + 0.07142857145 Combine like terms: -0.479157424 + 0.07142857145 = -0.40772885255 m = -0.40772885255 Simplifying m = -0.40772885255Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.55058599545, -0.40772885255}
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