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Simplifying m2 + -25m = 19 Reorder the terms: -25m + m2 = 19 Solving -25m + m2 = 19 Solving for variable 'm'. Reorder the terms: -19 + -25m + m2 = 19 + -19 Combine like terms: 19 + -19 = 0 -19 + -25m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '19' to each side of the equation. -19 + -25m + 19 + m2 = 0 + 19 Reorder the terms: -19 + 19 + -25m + m2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + -25m + m2 = 0 + 19 -25m + m2 = 0 + 19 Combine like terms: 0 + 19 = 19 -25m + m2 = 19 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 = 19 + 156.25 Reorder the terms: 156.25 + -25m + m2 = 19 + 156.25 Combine like terms: 19 + 156.25 = 175.25 156.25 + -25m + m2 = 175.25 Factor a perfect square on the left side: (m + -12.5)(m + -12.5) = 175.25 Calculate the square root of the right side: 13.238202295 Break this problem into two subproblems by setting (m + -12.5) equal to 13.238202295 and -13.238202295.Subproblem 1
m + -12.5 = 13.238202295 Simplifying m + -12.5 = 13.238202295 Reorder the terms: -12.5 + m = 13.238202295 Solving -12.5 + m = 13.238202295 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 = 13.238202295 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + m = 13.238202295 + 12.5 m = 13.238202295 + 12.5 Combine like terms: 13.238202295 + 12.5 = 25.738202295 m = 25.738202295 Simplifying m = 25.738202295Subproblem 2
m + -12.5 = -13.238202295 Simplifying m + -12.5 = -13.238202295 Reorder the terms: -12.5 + m = -13.238202295 Solving -12.5 + m = -13.238202295 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 = -13.238202295 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + m = -13.238202295 + 12.5 m = -13.238202295 + 12.5 Combine like terms: -13.238202295 + 12.5 = -0.738202295 m = -0.738202295 Simplifying m = -0.738202295Solution
The solution to the problem is based on the solutions from the subproblems. m = {25.738202295, -0.738202295}
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