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Simplifying m2 + -55m + -14 = 0 Reorder the terms: -14 + -55m + m2 = 0 Solving -14 + -55m + m2 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '14' to each side of the equation. -14 + -55m + 14 + m2 = 0 + 14 Reorder the terms: -14 + 14 + -55m + m2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + -55m + m2 = 0 + 14 -55m + m2 = 0 + 14 Combine like terms: 0 + 14 = 14 -55m + m2 = 14 The m term is -55m. Take half its coefficient (-27.5). Square it (756.25) and add it to both sides. Add '756.25' to each side of the equation. -55m + 756.25 + m2 = 14 + 756.25 Reorder the terms: 756.25 + -55m + m2 = 14 + 756.25 Combine like terms: 14 + 756.25 = 770.25 756.25 + -55m + m2 = 770.25 Factor a perfect square on the left side: (m + -27.5)(m + -27.5) = 770.25 Calculate the square root of the right side: 27.753378173 Break this problem into two subproblems by setting (m + -27.5) equal to 27.753378173 and -27.753378173.Subproblem 1
m + -27.5 = 27.753378173 Simplifying m + -27.5 = 27.753378173 Reorder the terms: -27.5 + m = 27.753378173 Solving -27.5 + m = 27.753378173 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '27.5' to each side of the equation. -27.5 + 27.5 + m = 27.753378173 + 27.5 Combine like terms: -27.5 + 27.5 = 0.0 0.0 + m = 27.753378173 + 27.5 m = 27.753378173 + 27.5 Combine like terms: 27.753378173 + 27.5 = 55.253378173 m = 55.253378173 Simplifying m = 55.253378173Subproblem 2
m + -27.5 = -27.753378173 Simplifying m + -27.5 = -27.753378173 Reorder the terms: -27.5 + m = -27.753378173 Solving -27.5 + m = -27.753378173 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '27.5' to each side of the equation. -27.5 + 27.5 + m = -27.753378173 + 27.5 Combine like terms: -27.5 + 27.5 = 0.0 0.0 + m = -27.753378173 + 27.5 m = -27.753378173 + 27.5 Combine like terms: -27.753378173 + 27.5 = -0.253378173 m = -0.253378173 Simplifying m = -0.253378173Solution
The solution to the problem is based on the solutions from the subproblems. m = {55.253378173, -0.253378173}
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