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Simplifying 20m2 + 23m + -6 = 0 Reorder the terms: -6 + 23m + 20m2 = 0 Solving -6 + 23m + 20m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -0.3 + 1.15m + m2 = 0 Move the constant term to the right: Add '0.3' to each side of the equation. -0.3 + 1.15m + 0.3 + m2 = 0 + 0.3 Reorder the terms: -0.3 + 0.3 + 1.15m + m2 = 0 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + 1.15m + m2 = 0 + 0.3 1.15m + m2 = 0 + 0.3 Combine like terms: 0 + 0.3 = 0.3 1.15m + m2 = 0.3 The m term is 1.15m. Take half its coefficient (0.575). Square it (0.330625) and add it to both sides. Add '0.330625' to each side of the equation. 1.15m + 0.330625 + m2 = 0.3 + 0.330625 Reorder the terms: 0.330625 + 1.15m + m2 = 0.3 + 0.330625 Combine like terms: 0.3 + 0.330625 = 0.630625 0.330625 + 1.15m + m2 = 0.630625 Factor a perfect square on the left side: (m + 0.575)(m + 0.575) = 0.630625 Calculate the square root of the right side: 0.794119009 Break this problem into two subproblems by setting (m + 0.575) equal to 0.794119009 and -0.794119009.Subproblem 1
m + 0.575 = 0.794119009 Simplifying m + 0.575 = 0.794119009 Reorder the terms: 0.575 + m = 0.794119009 Solving 0.575 + m = 0.794119009 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.575' to each side of the equation. 0.575 + -0.575 + m = 0.794119009 + -0.575 Combine like terms: 0.575 + -0.575 = 0.000 0.000 + m = 0.794119009 + -0.575 m = 0.794119009 + -0.575 Combine like terms: 0.794119009 + -0.575 = 0.219119009 m = 0.219119009 Simplifying m = 0.219119009Subproblem 2
m + 0.575 = -0.794119009 Simplifying m + 0.575 = -0.794119009 Reorder the terms: 0.575 + m = -0.794119009 Solving 0.575 + m = -0.794119009 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.575' to each side of the equation. 0.575 + -0.575 + m = -0.794119009 + -0.575 Combine like terms: 0.575 + -0.575 = 0.000 0.000 + m = -0.794119009 + -0.575 m = -0.794119009 + -0.575 Combine like terms: -0.794119009 + -0.575 = -1.369119009 m = -1.369119009 Simplifying m = -1.369119009Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.219119009, -1.369119009}
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