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Simplifying m2 = -13m + 42 Reorder the terms: m2 = 42 + -13m Solving m2 = 42 + -13m Solving for variable 'm'. Reorder the terms: -42 + 13m + m2 = 42 + -13m + -42 + 13m Reorder the terms: -42 + 13m + m2 = 42 + -42 + -13m + 13m Combine like terms: 42 + -42 = 0 -42 + 13m + m2 = 0 + -13m + 13m -42 + 13m + m2 = -13m + 13m Combine like terms: -13m + 13m = 0 -42 + 13m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '42' to each side of the equation. -42 + 13m + 42 + m2 = 0 + 42 Reorder the terms: -42 + 42 + 13m + m2 = 0 + 42 Combine like terms: -42 + 42 = 0 0 + 13m + m2 = 0 + 42 13m + m2 = 0 + 42 Combine like terms: 0 + 42 = 42 13m + m2 = 42 The m term is 13m. Take half its coefficient (6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. 13m + 42.25 + m2 = 42 + 42.25 Reorder the terms: 42.25 + 13m + m2 = 42 + 42.25 Combine like terms: 42 + 42.25 = 84.25 42.25 + 13m + m2 = 84.25 Factor a perfect square on the left side: (m + 6.5)(m + 6.5) = 84.25 Calculate the square root of the right side: 9.178779875 Break this problem into two subproblems by setting (m + 6.5) equal to 9.178779875 and -9.178779875.Subproblem 1
m + 6.5 = 9.178779875 Simplifying m + 6.5 = 9.178779875 Reorder the terms: 6.5 + m = 9.178779875 Solving 6.5 + m = 9.178779875 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + m = 9.178779875 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + m = 9.178779875 + -6.5 m = 9.178779875 + -6.5 Combine like terms: 9.178779875 + -6.5 = 2.678779875 m = 2.678779875 Simplifying m = 2.678779875Subproblem 2
m + 6.5 = -9.178779875 Simplifying m + 6.5 = -9.178779875 Reorder the terms: 6.5 + m = -9.178779875 Solving 6.5 + m = -9.178779875 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + m = -9.178779875 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + m = -9.178779875 + -6.5 m = -9.178779875 + -6.5 Combine like terms: -9.178779875 + -6.5 = -15.678779875 m = -15.678779875 Simplifying m = -15.678779875Solution
The solution to the problem is based on the solutions from the subproblems. m = {2.678779875, -15.678779875}
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