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Simplifying 2m2 + -25m + -90 = 0 Reorder the terms: -90 + -25m + 2m2 = 0 Solving -90 + -25m + 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'. -45 + -12.5m + m2 = 0 Move the constant term to the right: Add '45' to each side of the equation. -45 + -12.5m + 45 + m2 = 0 + 45 Reorder the terms: -45 + 45 + -12.5m + m2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + -12.5m + m2 = 0 + 45 -12.5m + m2 = 0 + 45 Combine like terms: 0 + 45 = 45 -12.5m + m2 = 45 The m term is -12.5m. Take half its coefficient (-6.25). Square it (39.0625) and add it to both sides. Add '39.0625' to each side of the equation. -12.5m + 39.0625 + m2 = 45 + 39.0625 Reorder the terms: 39.0625 + -12.5m + m2 = 45 + 39.0625 Combine like terms: 45 + 39.0625 = 84.0625 39.0625 + -12.5m + m2 = 84.0625 Factor a perfect square on the left side: (m + -6.25)(m + -6.25) = 84.0625 Calculate the square root of the right side: 9.16856041 Break this problem into two subproblems by setting (m + -6.25) equal to 9.16856041 and -9.16856041.Subproblem 1
m + -6.25 = 9.16856041 Simplifying m + -6.25 = 9.16856041 Reorder the terms: -6.25 + m = 9.16856041 Solving -6.25 + m = 9.16856041 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + m = 9.16856041 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + m = 9.16856041 + 6.25 m = 9.16856041 + 6.25 Combine like terms: 9.16856041 + 6.25 = 15.41856041 m = 15.41856041 Simplifying m = 15.41856041Subproblem 2
m + -6.25 = -9.16856041 Simplifying m + -6.25 = -9.16856041 Reorder the terms: -6.25 + m = -9.16856041 Solving -6.25 + m = -9.16856041 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + m = -9.16856041 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + m = -9.16856041 + 6.25 m = -9.16856041 + 6.25 Combine like terms: -9.16856041 + 6.25 = -2.91856041 m = -2.91856041 Simplifying m = -2.91856041Solution
The solution to the problem is based on the solutions from the subproblems. m = {15.41856041, -2.91856041}
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