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Simplifying 4m2 + -31m + -42 = 0 Reorder the terms: -42 + -31m + 4m2 = 0 Solving -42 + -31m + 4m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -10.5 + -7.75m + m2 = 0 Move the constant term to the right: Add '10.5' to each side of the equation. -10.5 + -7.75m + 10.5 + m2 = 0 + 10.5 Reorder the terms: -10.5 + 10.5 + -7.75m + m2 = 0 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + -7.75m + m2 = 0 + 10.5 -7.75m + m2 = 0 + 10.5 Combine like terms: 0 + 10.5 = 10.5 -7.75m + m2 = 10.5 The m term is -7.75m. Take half its coefficient (-3.875). Square it (15.015625) and add it to both sides. Add '15.015625' to each side of the equation. -7.75m + 15.015625 + m2 = 10.5 + 15.015625 Reorder the terms: 15.015625 + -7.75m + m2 = 10.5 + 15.015625 Combine like terms: 10.5 + 15.015625 = 25.515625 15.015625 + -7.75m + m2 = 25.515625 Factor a perfect square on the left side: (m + -3.875)(m + -3.875) = 25.515625 Calculate the square root of the right side: 5.051299338 Break this problem into two subproblems by setting (m + -3.875) equal to 5.051299338 and -5.051299338.Subproblem 1
m + -3.875 = 5.051299338 Simplifying m + -3.875 = 5.051299338 Reorder the terms: -3.875 + m = 5.051299338 Solving -3.875 + m = 5.051299338 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '3.875' to each side of the equation. -3.875 + 3.875 + m = 5.051299338 + 3.875 Combine like terms: -3.875 + 3.875 = 0.000 0.000 + m = 5.051299338 + 3.875 m = 5.051299338 + 3.875 Combine like terms: 5.051299338 + 3.875 = 8.926299338 m = 8.926299338 Simplifying m = 8.926299338Subproblem 2
m + -3.875 = -5.051299338 Simplifying m + -3.875 = -5.051299338 Reorder the terms: -3.875 + m = -5.051299338 Solving -3.875 + m = -5.051299338 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '3.875' to each side of the equation. -3.875 + 3.875 + m = -5.051299338 + 3.875 Combine like terms: -3.875 + 3.875 = 0.000 0.000 + m = -5.051299338 + 3.875 m = -5.051299338 + 3.875 Combine like terms: -5.051299338 + 3.875 = -1.176299338 m = -1.176299338 Simplifying m = -1.176299338Solution
The solution to the problem is based on the solutions from the subproblems. m = {8.926299338, -1.176299338}
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