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Simplifying 8m2 + 86m + 117 = 0 Reorder the terms: 117 + 86m + 8m2 = 0 Solving 117 + 86m + 8m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 14.625 + 10.75m + m2 = 0 Move the constant term to the right: Add '-14.625' to each side of the equation. 14.625 + 10.75m + -14.625 + m2 = 0 + -14.625 Reorder the terms: 14.625 + -14.625 + 10.75m + m2 = 0 + -14.625 Combine like terms: 14.625 + -14.625 = 0.000 0.000 + 10.75m + m2 = 0 + -14.625 10.75m + m2 = 0 + -14.625 Combine like terms: 0 + -14.625 = -14.625 10.75m + m2 = -14.625 The m term is 10.75m. Take half its coefficient (5.375). Square it (28.890625) and add it to both sides. Add '28.890625' to each side of the equation. 10.75m + 28.890625 + m2 = -14.625 + 28.890625 Reorder the terms: 28.890625 + 10.75m + m2 = -14.625 + 28.890625 Combine like terms: -14.625 + 28.890625 = 14.265625 28.890625 + 10.75m + m2 = 14.265625 Factor a perfect square on the left side: (m + 5.375)(m + 5.375) = 14.265625 Calculate the square root of the right side: 3.776986232 Break this problem into two subproblems by setting (m + 5.375) equal to 3.776986232 and -3.776986232.Subproblem 1
m + 5.375 = 3.776986232 Simplifying m + 5.375 = 3.776986232 Reorder the terms: 5.375 + m = 3.776986232 Solving 5.375 + m = 3.776986232 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-5.375' to each side of the equation. 5.375 + -5.375 + m = 3.776986232 + -5.375 Combine like terms: 5.375 + -5.375 = 0.000 0.000 + m = 3.776986232 + -5.375 m = 3.776986232 + -5.375 Combine like terms: 3.776986232 + -5.375 = -1.598013768 m = -1.598013768 Simplifying m = -1.598013768Subproblem 2
m + 5.375 = -3.776986232 Simplifying m + 5.375 = -3.776986232 Reorder the terms: 5.375 + m = -3.776986232 Solving 5.375 + m = -3.776986232 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-5.375' to each side of the equation. 5.375 + -5.375 + m = -3.776986232 + -5.375 Combine like terms: 5.375 + -5.375 = 0.000 0.000 + m = -3.776986232 + -5.375 m = -3.776986232 + -5.375 Combine like terms: -3.776986232 + -5.375 = -9.151986232 m = -9.151986232 Simplifying m = -9.151986232Solution
The solution to the problem is based on the solutions from the subproblems. m = {-1.598013768, -9.151986232}
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