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Simplifying -2m(4m + 1) * 5 = -13 Reorder the terms: -2m(1 + 4m) * 5 = -13 Reorder the terms for easier multiplication: -2 * 5m(1 + 4m) = -13 Multiply -2 * 5 -10m(1 + 4m) = -13 (1 * -10m + 4m * -10m) = -13 (-10m + -40m2) = -13 Solving -10m + -40m2 = -13 Solving for variable 'm'. Reorder the terms: 13 + -10m + -40m2 = -13 + 13 Combine like terms: -13 + 13 = 0 13 + -10m + -40m2 = 0 Begin completing the square. Divide all terms by -40 the coefficient of the squared term: Divide each side by '-40'. -0.325 + 0.25m + m2 = 0.0 Move the constant term to the right: Add '0.325' to each side of the equation. -0.325 + 0.25m + 0.325 + m2 = 0.0 + 0.325 Reorder the terms: -0.325 + 0.325 + 0.25m + m2 = 0.0 + 0.325 Combine like terms: -0.325 + 0.325 = 0.000 0.000 + 0.25m + m2 = 0.0 + 0.325 0.25m + m2 = 0.0 + 0.325 Combine like terms: 0.0 + 0.325 = 0.325 0.25m + m2 = 0.325 The m term is 0.25m. Take half its coefficient (0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. 0.25m + 0.015625 + m2 = 0.325 + 0.015625 Reorder the terms: 0.015625 + 0.25m + m2 = 0.325 + 0.015625 Combine like terms: 0.325 + 0.015625 = 0.340625 0.015625 + 0.25m + m2 = 0.340625 Factor a perfect square on the left side: (m + 0.125)(m + 0.125) = 0.340625 Calculate the square root of the right side: 0.583630876 Break this problem into two subproblems by setting (m + 0.125) equal to 0.583630876 and -0.583630876.Subproblem 1
m + 0.125 = 0.583630876 Simplifying m + 0.125 = 0.583630876 Reorder the terms: 0.125 + m = 0.583630876 Solving 0.125 + m = 0.583630876 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + m = 0.583630876 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + m = 0.583630876 + -0.125 m = 0.583630876 + -0.125 Combine like terms: 0.583630876 + -0.125 = 0.458630876 m = 0.458630876 Simplifying m = 0.458630876Subproblem 2
m + 0.125 = -0.583630876 Simplifying m + 0.125 = -0.583630876 Reorder the terms: 0.125 + m = -0.583630876 Solving 0.125 + m = -0.583630876 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + m = -0.583630876 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + m = -0.583630876 + -0.125 m = -0.583630876 + -0.125 Combine like terms: -0.583630876 + -0.125 = -0.708630876 m = -0.708630876 Simplifying m = -0.708630876Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.458630876, -0.708630876}
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