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Simplifying [(7m2 + 5m + -5) + -1(5m2 + -3m + 8)] + -1(m2 + m + 3) = 0 Reorder the terms: [(-5 + 5m + 7m2) + -1(5m2 + -3m + 8)] + -1(m2 + m + 3) = 0 Remove parenthesis around (-5 + 5m + 7m2) [-5 + 5m + 7m2 + -1(5m2 + -3m + 8)] + -1(m2 + m + 3) = 0 Reorder the terms: [-5 + 5m + 7m2 + -1(8 + -3m + 5m2)] + -1(m2 + m + 3) = 0 [-5 + 5m + 7m2 + (8 * -1 + -3m * -1 + 5m2 * -1)] + -1(m2 + m + 3) = 0 [-5 + 5m + 7m2 + (-8 + 3m + -5m2)] + -1(m2 + m + 3) = 0 Reorder the terms: [-5 + -8 + 5m + 3m + 7m2 + -5m2] + -1(m2 + m + 3) = 0 Combine like terms: -5 + -8 = -13 [-13 + 5m + 3m + 7m2 + -5m2] + -1(m2 + m + 3) = 0 Combine like terms: 5m + 3m = 8m [-13 + 8m + 7m2 + -5m2] + -1(m2 + m + 3) = 0 Combine like terms: 7m2 + -5m2 = 2m2 [-13 + 8m + 2m2] + -1(m2 + m + 3) = 0 Remove brackets around [-13 + 8m + 2m2] -13 + 8m + 2m2 + -1(m2 + m + 3) = 0 Reorder the terms: -13 + 8m + 2m2 + -1(3 + m + m2) = 0 -13 + 8m + 2m2 + (3 * -1 + m * -1 + m2 * -1) = 0 -13 + 8m + 2m2 + (-3 + -1m + -1m2) = 0 Reorder the terms: -13 + -3 + 8m + -1m + 2m2 + -1m2 = 0 Combine like terms: -13 + -3 = -16 -16 + 8m + -1m + 2m2 + -1m2 = 0 Combine like terms: 8m + -1m = 7m -16 + 7m + 2m2 + -1m2 = 0 Combine like terms: 2m2 + -1m2 = 1m2 -16 + 7m + 1m2 = 0 Solving -16 + 7m + 1m2 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + 7m + 16 + m2 = 0 + 16 Reorder the terms: -16 + 16 + 7m + m2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 7m + m2 = 0 + 16 7m + m2 = 0 + 16 Combine like terms: 0 + 16 = 16 7m + m2 = 16 The m term is 7m. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7m + 12.25 + m2 = 16 + 12.25 Reorder the terms: 12.25 + 7m + m2 = 16 + 12.25 Combine like terms: 16 + 12.25 = 28.25 12.25 + 7m + m2 = 28.25 Factor a perfect square on the left side: (m + 3.5)(m + 3.5) = 28.25 Calculate the square root of the right side: 5.315072906 Break this problem into two subproblems by setting (m + 3.5) equal to 5.315072906 and -5.315072906.Subproblem 1
m + 3.5 = 5.315072906 Simplifying m + 3.5 = 5.315072906 Reorder the terms: 3.5 + m = 5.315072906 Solving 3.5 + m = 5.315072906 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + m = 5.315072906 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + m = 5.315072906 + -3.5 m = 5.315072906 + -3.5 Combine like terms: 5.315072906 + -3.5 = 1.815072906 m = 1.815072906 Simplifying m = 1.815072906Subproblem 2
m + 3.5 = -5.315072906 Simplifying m + 3.5 = -5.315072906 Reorder the terms: 3.5 + m = -5.315072906 Solving 3.5 + m = -5.315072906 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + m = -5.315072906 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + m = -5.315072906 + -3.5 m = -5.315072906 + -3.5 Combine like terms: -5.315072906 + -3.5 = -8.815072906 m = -8.815072906 Simplifying m = -8.815072906Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.815072906, -8.815072906}
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