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Simplifying m2 + -25m + 120 = 0 Reorder the terms: 120 + -25m + m2 = 0 Solving 120 + -25m + m2 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '-120' to each side of the equation. 120 + -25m + -120 + m2 = 0 + -120 Reorder the terms: 120 + -120 + -25m + m2 = 0 + -120 Combine like terms: 120 + -120 = 0 0 + -25m + m2 = 0 + -120 -25m + m2 = 0 + -120 Combine like terms: 0 + -120 = -120 -25m + m2 = -120 The m term is -25m. Take half its coefficient (-12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. -25m + 156.25 + m2 = -120 + 156.25 Reorder the terms: 156.25 + -25m + m2 = -120 + 156.25 Combine like terms: -120 + 156.25 = 36.25 156.25 + -25m + m2 = 36.25 Factor a perfect square on the left side: (m + -12.5)(m + -12.5) = 36.25 Calculate the square root of the right side: 6.020797289 Break this problem into two subproblems by setting (m + -12.5) equal to 6.020797289 and -6.020797289.Subproblem 1
m + -12.5 = 6.020797289 Simplifying m + -12.5 = 6.020797289 Reorder the terms: -12.5 + m = 6.020797289 Solving -12.5 + m = 6.020797289 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + m = 6.020797289 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + m = 6.020797289 + 12.5 m = 6.020797289 + 12.5 Combine like terms: 6.020797289 + 12.5 = 18.520797289 m = 18.520797289 Simplifying m = 18.520797289Subproblem 2
m + -12.5 = -6.020797289 Simplifying m + -12.5 = -6.020797289 Reorder the terms: -12.5 + m = -6.020797289 Solving -12.5 + m = -6.020797289 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + m = -6.020797289 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + m = -6.020797289 + 12.5 m = -6.020797289 + 12.5 Combine like terms: -6.020797289 + 12.5 = 6.479202711 m = 6.479202711 Simplifying m = 6.479202711Solution
The solution to the problem is based on the solutions from the subproblems. m = {18.520797289, 6.479202711}
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