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Simplifying 2m2 + -5m = 14 Reorder the terms: -5m + 2m2 = 14 Solving -5m + 2m2 = 14 Solving for variable 'm'. Reorder the terms: -14 + -5m + 2m2 = 14 + -14 Combine like terms: 14 + -14 = 0 -14 + -5m + 2m2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -7 + -2.5m + m2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + -2.5m + 7 + m2 = 0 + 7 Reorder the terms: -7 + 7 + -2.5m + m2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -2.5m + m2 = 0 + 7 -2.5m + m2 = 0 + 7 Combine like terms: 0 + 7 = 7 -2.5m + m2 = 7 The m term is -2.5m. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5m + 1.5625 + m2 = 7 + 1.5625 Reorder the terms: 1.5625 + -2.5m + m2 = 7 + 1.5625 Combine like terms: 7 + 1.5625 = 8.5625 1.5625 + -2.5m + m2 = 8.5625 Factor a perfect square on the left side: (m + -1.25)(m + -1.25) = 8.5625 Calculate the square root of the right side: 2.926174978 Break this problem into two subproblems by setting (m + -1.25) equal to 2.926174978 and -2.926174978.Subproblem 1
m + -1.25 = 2.926174978 Simplifying m + -1.25 = 2.926174978 Reorder the terms: -1.25 + m = 2.926174978 Solving -1.25 + m = 2.926174978 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + m = 2.926174978 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + m = 2.926174978 + 1.25 m = 2.926174978 + 1.25 Combine like terms: 2.926174978 + 1.25 = 4.176174978 m = 4.176174978 Simplifying m = 4.176174978Subproblem 2
m + -1.25 = -2.926174978 Simplifying m + -1.25 = -2.926174978 Reorder the terms: -1.25 + m = -2.926174978 Solving -1.25 + m = -2.926174978 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + m = -2.926174978 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + m = -2.926174978 + 1.25 m = -2.926174978 + 1.25 Combine like terms: -2.926174978 + 1.25 = -1.676174978 m = -1.676174978 Simplifying m = -1.676174978Solution
The solution to the problem is based on the solutions from the subproblems. m = {4.176174978, -1.676174978}
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