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Simplifying 63m2 + -31m + -63 = 0 Reorder the terms: -63 + -31m + 63m2 = 0 Solving -63 + -31m + 63m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 63 the coefficient of the squared term: Divide each side by '63'. -1 + -0.4920634921m + m2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -0.4920634921m + 1 + m2 = 0 + 1 Reorder the terms: -1 + 1 + -0.4920634921m + m2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -0.4920634921m + m2 = 0 + 1 -0.4920634921m + m2 = 0 + 1 Combine like terms: 0 + 1 = 1 -0.4920634921m + m2 = 1 The m term is -0.4920634921m. Take half its coefficient (-0.2460317461). Square it (0.06053162009) and add it to both sides. Add '0.06053162009' to each side of the equation. -0.4920634921m + 0.06053162009 + m2 = 1 + 0.06053162009 Reorder the terms: 0.06053162009 + -0.4920634921m + m2 = 1 + 0.06053162009 Combine like terms: 1 + 0.06053162009 = 1.06053162009 0.06053162009 + -0.4920634921m + m2 = 1.06053162009 Factor a perfect square on the left side: (m + -0.2460317461)(m + -0.2460317461) = 1.06053162009 Calculate the square root of the right side: 1.029821159 Break this problem into two subproblems by setting (m + -0.2460317461) equal to 1.029821159 and -1.029821159.Subproblem 1
m + -0.2460317461 = 1.029821159 Simplifying m + -0.2460317461 = 1.029821159 Reorder the terms: -0.2460317461 + m = 1.029821159 Solving -0.2460317461 + m = 1.029821159 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.2460317461' to each side of the equation. -0.2460317461 + 0.2460317461 + m = 1.029821159 + 0.2460317461 Combine like terms: -0.2460317461 + 0.2460317461 = 0.0000000000 0.0000000000 + m = 1.029821159 + 0.2460317461 m = 1.029821159 + 0.2460317461 Combine like terms: 1.029821159 + 0.2460317461 = 1.2758529051 m = 1.2758529051 Simplifying m = 1.2758529051Subproblem 2
m + -0.2460317461 = -1.029821159 Simplifying m + -0.2460317461 = -1.029821159 Reorder the terms: -0.2460317461 + m = -1.029821159 Solving -0.2460317461 + m = -1.029821159 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.2460317461' to each side of the equation. -0.2460317461 + 0.2460317461 + m = -1.029821159 + 0.2460317461 Combine like terms: -0.2460317461 + 0.2460317461 = 0.0000000000 0.0000000000 + m = -1.029821159 + 0.2460317461 m = -1.029821159 + 0.2460317461 Combine like terms: -1.029821159 + 0.2460317461 = -0.7837894129 m = -0.7837894129 Simplifying m = -0.7837894129Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.2758529051, -0.7837894129}
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