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Simplifying (10m2 + 5m + -9) + -1(8m2 + -3m + 5) + -1(m2 + m + 7) = 0 Reorder the terms: (-9 + 5m + 10m2) + -1(8m2 + -3m + 5) + -1(m2 + m + 7) = 0 Remove parenthesis around (-9 + 5m + 10m2) -9 + 5m + 10m2 + -1(8m2 + -3m + 5) + -1(m2 + m + 7) = 0 Reorder the terms: -9 + 5m + 10m2 + -1(5 + -3m + 8m2) + -1(m2 + m + 7) = 0 -9 + 5m + 10m2 + (5 * -1 + -3m * -1 + 8m2 * -1) + -1(m2 + m + 7) = 0 -9 + 5m + 10m2 + (-5 + 3m + -8m2) + -1(m2 + m + 7) = 0 Reorder the terms: -9 + 5m + 10m2 + -5 + 3m + -8m2 + -1(7 + m + m2) = 0 -9 + 5m + 10m2 + -5 + 3m + -8m2 + (7 * -1 + m * -1 + m2 * -1) = 0 -9 + 5m + 10m2 + -5 + 3m + -8m2 + (-7 + -1m + -1m2) = 0 Reorder the terms: -9 + -5 + -7 + 5m + 3m + -1m + 10m2 + -8m2 + -1m2 = 0 Combine like terms: -9 + -5 = -14 -14 + -7 + 5m + 3m + -1m + 10m2 + -8m2 + -1m2 = 0 Combine like terms: -14 + -7 = -21 -21 + 5m + 3m + -1m + 10m2 + -8m2 + -1m2 = 0 Combine like terms: 5m + 3m = 8m -21 + 8m + -1m + 10m2 + -8m2 + -1m2 = 0 Combine like terms: 8m + -1m = 7m -21 + 7m + 10m2 + -8m2 + -1m2 = 0 Combine like terms: 10m2 + -8m2 = 2m2 -21 + 7m + 2m2 + -1m2 = 0 Combine like terms: 2m2 + -1m2 = 1m2 -21 + 7m + 1m2 = 0 Solving -21 + 7m + 1m2 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '21' to each side of the equation. -21 + 7m + 21 + m2 = 0 + 21 Reorder the terms: -21 + 21 + 7m + m2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + 7m + m2 = 0 + 21 7m + m2 = 0 + 21 Combine like terms: 0 + 21 = 21 7m + m2 = 21 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 = 21 + 12.25 Reorder the terms: 12.25 + 7m + m2 = 21 + 12.25 Combine like terms: 21 + 12.25 = 33.25 12.25 + 7m + m2 = 33.25 Factor a perfect square on the left side: (m + 3.5)(m + 3.5) = 33.25 Calculate the square root of the right side: 5.766281297 Break this problem into two subproblems by setting (m + 3.5) equal to 5.766281297 and -5.766281297.Subproblem 1
m + 3.5 = 5.766281297 Simplifying m + 3.5 = 5.766281297 Reorder the terms: 3.5 + m = 5.766281297 Solving 3.5 + m = 5.766281297 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 = 5.766281297 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + m = 5.766281297 + -3.5 m = 5.766281297 + -3.5 Combine like terms: 5.766281297 + -3.5 = 2.266281297 m = 2.266281297 Simplifying m = 2.266281297Subproblem 2
m + 3.5 = -5.766281297 Simplifying m + 3.5 = -5.766281297 Reorder the terms: 3.5 + m = -5.766281297 Solving 3.5 + m = -5.766281297 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 = -5.766281297 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + m = -5.766281297 + -3.5 m = -5.766281297 + -3.5 Combine like terms: -5.766281297 + -3.5 = -9.266281297 m = -9.266281297 Simplifying m = -9.266281297Solution
The solution to the problem is based on the solutions from the subproblems. m = {2.266281297, -9.266281297}
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