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Simplifying 2m2 + -15m + -26 = 0 Reorder the terms: -26 + -15m + 2m2 = 0 Solving -26 + -15m + 2m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -13 + -7.5m + m2 = 0 Move the constant term to the right: Add '13' to each side of the equation. -13 + -7.5m + 13 + m2 = 0 + 13 Reorder the terms: -13 + 13 + -7.5m + m2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -7.5m + m2 = 0 + 13 -7.5m + m2 = 0 + 13 Combine like terms: 0 + 13 = 13 -7.5m + m2 = 13 The m term is -7.5m. Take half its coefficient (-3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. -7.5m + 14.0625 + m2 = 13 + 14.0625 Reorder the terms: 14.0625 + -7.5m + m2 = 13 + 14.0625 Combine like terms: 13 + 14.0625 = 27.0625 14.0625 + -7.5m + m2 = 27.0625 Factor a perfect square on the left side: (m + -3.75)(m + -3.75) = 27.0625 Calculate the square root of the right side: 5.202163012 Break this problem into two subproblems by setting (m + -3.75) equal to 5.202163012 and -5.202163012.Subproblem 1
m + -3.75 = 5.202163012 Simplifying m + -3.75 = 5.202163012 Reorder the terms: -3.75 + m = 5.202163012 Solving -3.75 + m = 5.202163012 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + m = 5.202163012 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + m = 5.202163012 + 3.75 m = 5.202163012 + 3.75 Combine like terms: 5.202163012 + 3.75 = 8.952163012 m = 8.952163012 Simplifying m = 8.952163012Subproblem 2
m + -3.75 = -5.202163012 Simplifying m + -3.75 = -5.202163012 Reorder the terms: -3.75 + m = -5.202163012 Solving -3.75 + m = -5.202163012 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + m = -5.202163012 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + m = -5.202163012 + 3.75 m = -5.202163012 + 3.75 Combine like terms: -5.202163012 + 3.75 = -1.452163012 m = -1.452163012 Simplifying m = -1.452163012Solution
The solution to the problem is based on the solutions from the subproblems. m = {8.952163012, -1.452163012}
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