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Simplifying 2m2 + -8m + -47 = 0 Reorder the terms: -47 + -8m + 2m2 = 0 Solving -47 + -8m + 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'. -23.5 + -4m + m2 = 0 Move the constant term to the right: Add '23.5' to each side of the equation. -23.5 + -4m + 23.5 + m2 = 0 + 23.5 Reorder the terms: -23.5 + 23.5 + -4m + m2 = 0 + 23.5 Combine like terms: -23.5 + 23.5 = 0.0 0.0 + -4m + m2 = 0 + 23.5 -4m + m2 = 0 + 23.5 Combine like terms: 0 + 23.5 = 23.5 -4m + m2 = 23.5 The m term is -4m. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4m + 4 + m2 = 23.5 + 4 Reorder the terms: 4 + -4m + m2 = 23.5 + 4 Combine like terms: 23.5 + 4 = 27.5 4 + -4m + m2 = 27.5 Factor a perfect square on the left side: (m + -2)(m + -2) = 27.5 Calculate the square root of the right side: 5.244044241 Break this problem into two subproblems by setting (m + -2) equal to 5.244044241 and -5.244044241.Subproblem 1
m + -2 = 5.244044241 Simplifying m + -2 = 5.244044241 Reorder the terms: -2 + m = 5.244044241 Solving -2 + m = 5.244044241 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + m = 5.244044241 + 2 Combine like terms: -2 + 2 = 0 0 + m = 5.244044241 + 2 m = 5.244044241 + 2 Combine like terms: 5.244044241 + 2 = 7.244044241 m = 7.244044241 Simplifying m = 7.244044241Subproblem 2
m + -2 = -5.244044241 Simplifying m + -2 = -5.244044241 Reorder the terms: -2 + m = -5.244044241 Solving -2 + m = -5.244044241 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + m = -5.244044241 + 2 Combine like terms: -2 + 2 = 0 0 + m = -5.244044241 + 2 m = -5.244044241 + 2 Combine like terms: -5.244044241 + 2 = -3.244044241 m = -3.244044241 Simplifying m = -3.244044241Solution
The solution to the problem is based on the solutions from the subproblems. m = {7.244044241, -3.244044241}
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