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Simplifying 2 = 8m2 + -7m Reorder the terms: 2 = -7m + 8m2 Solving 2 = -7m + 8m2 Solving for variable 'm'. Reorder the terms: 2 + 7m + -8m2 = -7m + 7m + 8m2 + -8m2 Combine like terms: -7m + 7m = 0 2 + 7m + -8m2 = 0 + 8m2 + -8m2 2 + 7m + -8m2 = 8m2 + -8m2 Combine like terms: 8m2 + -8m2 = 0 2 + 7m + -8m2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -0.25 + -0.875m + m2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -0.875m + 0.25 + m2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -0.875m + m2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -0.875m + m2 = 0 + 0.25 -0.875m + m2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -0.875m + m2 = 0.25 The m term is -0.875m. Take half its coefficient (-0.4375). Square it (0.19140625) and add it to both sides. Add '0.19140625' to each side of the equation. -0.875m + 0.19140625 + m2 = 0.25 + 0.19140625 Reorder the terms: 0.19140625 + -0.875m + m2 = 0.25 + 0.19140625 Combine like terms: 0.25 + 0.19140625 = 0.44140625 0.19140625 + -0.875m + m2 = 0.44140625 Factor a perfect square on the left side: (m + -0.4375)(m + -0.4375) = 0.44140625 Calculate the square root of the right side: 0.664384113 Break this problem into two subproblems by setting (m + -0.4375) equal to 0.664384113 and -0.664384113.Subproblem 1
m + -0.4375 = 0.664384113 Simplifying m + -0.4375 = 0.664384113 Reorder the terms: -0.4375 + m = 0.664384113 Solving -0.4375 + m = 0.664384113 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.4375' to each side of the equation. -0.4375 + 0.4375 + m = 0.664384113 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + m = 0.664384113 + 0.4375 m = 0.664384113 + 0.4375 Combine like terms: 0.664384113 + 0.4375 = 1.101884113 m = 1.101884113 Simplifying m = 1.101884113Subproblem 2
m + -0.4375 = -0.664384113 Simplifying m + -0.4375 = -0.664384113 Reorder the terms: -0.4375 + m = -0.664384113 Solving -0.4375 + m = -0.664384113 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.4375' to each side of the equation. -0.4375 + 0.4375 + m = -0.664384113 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + m = -0.664384113 + 0.4375 m = -0.664384113 + 0.4375 Combine like terms: -0.664384113 + 0.4375 = -0.226884113 m = -0.226884113 Simplifying m = -0.226884113Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.101884113, -0.226884113}
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