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Simplifying (3m2 + -1m + -1) + -1(2m2 + 5m + -3) = 0 Reorder the terms: (-1 + -1m + 3m2) + -1(2m2 + 5m + -3) = 0 Remove parenthesis around (-1 + -1m + 3m2) -1 + -1m + 3m2 + -1(2m2 + 5m + -3) = 0 Reorder the terms: -1 + -1m + 3m2 + -1(-3 + 5m + 2m2) = 0 -1 + -1m + 3m2 + (-3 * -1 + 5m * -1 + 2m2 * -1) = 0 -1 + -1m + 3m2 + (3 + -5m + -2m2) = 0 Reorder the terms: -1 + 3 + -1m + -5m + 3m2 + -2m2 = 0 Combine like terms: -1 + 3 = 2 2 + -1m + -5m + 3m2 + -2m2 = 0 Combine like terms: -1m + -5m = -6m 2 + -6m + 3m2 + -2m2 = 0 Combine like terms: 3m2 + -2m2 = 1m2 2 + -6m + 1m2 = 0 Solving 2 + -6m + 1m2 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + -6m + -2 + m2 = 0 + -2 Reorder the terms: 2 + -2 + -6m + m2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -6m + m2 = 0 + -2 -6m + m2 = 0 + -2 Combine like terms: 0 + -2 = -2 -6m + m2 = -2 The m term is -6m. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6m + 9 + m2 = -2 + 9 Reorder the terms: 9 + -6m + m2 = -2 + 9 Combine like terms: -2 + 9 = 7 9 + -6m + m2 = 7 Factor a perfect square on the left side: (m + -3)(m + -3) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (m + -3) equal to 2.645751311 and -2.645751311.Subproblem 1
m + -3 = 2.645751311 Simplifying m + -3 = 2.645751311 Reorder the terms: -3 + m = 2.645751311 Solving -3 + m = 2.645751311 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + m = 2.645751311 + 3 Combine like terms: -3 + 3 = 0 0 + m = 2.645751311 + 3 m = 2.645751311 + 3 Combine like terms: 2.645751311 + 3 = 5.645751311 m = 5.645751311 Simplifying m = 5.645751311Subproblem 2
m + -3 = -2.645751311 Simplifying m + -3 = -2.645751311 Reorder the terms: -3 + m = -2.645751311 Solving -3 + m = -2.645751311 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + m = -2.645751311 + 3 Combine like terms: -3 + 3 = 0 0 + m = -2.645751311 + 3 m = -2.645751311 + 3 Combine like terms: -2.645751311 + 3 = 0.354248689 m = 0.354248689 Simplifying m = 0.354248689Solution
The solution to the problem is based on the solutions from the subproblems. m = {5.645751311, 0.354248689}
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