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Simplifying m2 + -9m + -55 = 0 Reorder the terms: -55 + -9m + m2 = 0 Solving -55 + -9m + m2 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '55' to each side of the equation. -55 + -9m + 55 + m2 = 0 + 55 Reorder the terms: -55 + 55 + -9m + m2 = 0 + 55 Combine like terms: -55 + 55 = 0 0 + -9m + m2 = 0 + 55 -9m + m2 = 0 + 55 Combine like terms: 0 + 55 = 55 -9m + m2 = 55 The m term is -9m. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9m + 20.25 + m2 = 55 + 20.25 Reorder the terms: 20.25 + -9m + m2 = 55 + 20.25 Combine like terms: 55 + 20.25 = 75.25 20.25 + -9m + m2 = 75.25 Factor a perfect square on the left side: (m + -4.5)(m + -4.5) = 75.25 Calculate the square root of the right side: 8.674675786 Break this problem into two subproblems by setting (m + -4.5) equal to 8.674675786 and -8.674675786.Subproblem 1
m + -4.5 = 8.674675786 Simplifying m + -4.5 = 8.674675786 Reorder the terms: -4.5 + m = 8.674675786 Solving -4.5 + m = 8.674675786 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + m = 8.674675786 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + m = 8.674675786 + 4.5 m = 8.674675786 + 4.5 Combine like terms: 8.674675786 + 4.5 = 13.174675786 m = 13.174675786 Simplifying m = 13.174675786Subproblem 2
m + -4.5 = -8.674675786 Simplifying m + -4.5 = -8.674675786 Reorder the terms: -4.5 + m = -8.674675786 Solving -4.5 + m = -8.674675786 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + m = -8.674675786 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + m = -8.674675786 + 4.5 m = -8.674675786 + 4.5 Combine like terms: -8.674675786 + 4.5 = -4.174675786 m = -4.174675786 Simplifying m = -4.174675786Solution
The solution to the problem is based on the solutions from the subproblems. m = {13.174675786, -4.174675786}
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