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Simplifying (8m2 + 5m + -2) + -1(8m + -2m + 9) = 0 Reorder the terms: (-2 + 5m + 8m2) + -1(8m + -2m + 9) = 0 Remove parenthesis around (-2 + 5m + 8m2) -2 + 5m + 8m2 + -1(8m + -2m + 9) = 0 Reorder the terms: -2 + 5m + 8m2 + -1(9 + 8m + -2m) = 0 Combine like terms: 8m + -2m = 6m -2 + 5m + 8m2 + -1(9 + 6m) = 0 -2 + 5m + 8m2 + (9 * -1 + 6m * -1) = 0 -2 + 5m + 8m2 + (-9 + -6m) = 0 Reorder the terms: -2 + -9 + 5m + -6m + 8m2 = 0 Combine like terms: -2 + -9 = -11 -11 + 5m + -6m + 8m2 = 0 Combine like terms: 5m + -6m = -1m -11 + -1m + 8m2 = 0 Solving -11 + -1m + 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'. -1.375 + -0.125m + m2 = 0 Move the constant term to the right: Add '1.375' to each side of the equation. -1.375 + -0.125m + 1.375 + m2 = 0 + 1.375 Reorder the terms: -1.375 + 1.375 + -0.125m + m2 = 0 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + -0.125m + m2 = 0 + 1.375 -0.125m + m2 = 0 + 1.375 Combine like terms: 0 + 1.375 = 1.375 -0.125m + m2 = 1.375 The m term is -0.125m. Take half its coefficient (-0.0625). Square it (0.00390625) and add it to both sides. Add '0.00390625' to each side of the equation. -0.125m + 0.00390625 + m2 = 1.375 + 0.00390625 Reorder the terms: 0.00390625 + -0.125m + m2 = 1.375 + 0.00390625 Combine like terms: 1.375 + 0.00390625 = 1.37890625 0.00390625 + -0.125m + m2 = 1.37890625 Factor a perfect square on the left side: (m + -0.0625)(m + -0.0625) = 1.37890625 Calculate the square root of the right side: 1.174268389 Break this problem into two subproblems by setting (m + -0.0625) equal to 1.174268389 and -1.174268389.Subproblem 1
m + -0.0625 = 1.174268389 Simplifying m + -0.0625 = 1.174268389 Reorder the terms: -0.0625 + m = 1.174268389 Solving -0.0625 + m = 1.174268389 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.0625' to each side of the equation. -0.0625 + 0.0625 + m = 1.174268389 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + m = 1.174268389 + 0.0625 m = 1.174268389 + 0.0625 Combine like terms: 1.174268389 + 0.0625 = 1.236768389 m = 1.236768389 Simplifying m = 1.236768389Subproblem 2
m + -0.0625 = -1.174268389 Simplifying m + -0.0625 = -1.174268389 Reorder the terms: -0.0625 + m = -1.174268389 Solving -0.0625 + m = -1.174268389 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.0625' to each side of the equation. -0.0625 + 0.0625 + m = -1.174268389 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + m = -1.174268389 + 0.0625 m = -1.174268389 + 0.0625 Combine like terms: -1.174268389 + 0.0625 = -1.111768389 m = -1.111768389 Simplifying m = -1.111768389Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.236768389, -1.111768389}
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