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Simplifying 2m2 + -10m + -3 = 0 Reorder the terms: -3 + -10m + 2m2 = 0 Solving -3 + -10m + 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'. -1.5 + -5m + m2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -5m + 1.5 + m2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + -5m + m2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -5m + m2 = 0 + 1.5 -5m + m2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 -5m + m2 = 1.5 The m term is -5m. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5m + 6.25 + m2 = 1.5 + 6.25 Reorder the terms: 6.25 + -5m + m2 = 1.5 + 6.25 Combine like terms: 1.5 + 6.25 = 7.75 6.25 + -5m + m2 = 7.75 Factor a perfect square on the left side: (m + -2.5)(m + -2.5) = 7.75 Calculate the square root of the right side: 2.783882181 Break this problem into two subproblems by setting (m + -2.5) equal to 2.783882181 and -2.783882181.Subproblem 1
m + -2.5 = 2.783882181 Simplifying m + -2.5 = 2.783882181 Reorder the terms: -2.5 + m = 2.783882181 Solving -2.5 + m = 2.783882181 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + m = 2.783882181 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + m = 2.783882181 + 2.5 m = 2.783882181 + 2.5 Combine like terms: 2.783882181 + 2.5 = 5.283882181 m = 5.283882181 Simplifying m = 5.283882181Subproblem 2
m + -2.5 = -2.783882181 Simplifying m + -2.5 = -2.783882181 Reorder the terms: -2.5 + m = -2.783882181 Solving -2.5 + m = -2.783882181 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + m = -2.783882181 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + m = -2.783882181 + 2.5 m = -2.783882181 + 2.5 Combine like terms: -2.783882181 + 2.5 = -0.283882181 m = -0.283882181 Simplifying m = -0.283882181Solution
The solution to the problem is based on the solutions from the subproblems. m = {5.283882181, -0.283882181}
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