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Simplifying (7u2 + -4u + -2) + (-5u + 1) = 0 Reorder the terms: (-2 + -4u + 7u2) + (-5u + 1) = 0 Remove parenthesis around (-2 + -4u + 7u2) -2 + -4u + 7u2 + (-5u + 1) = 0 Reorder the terms: -2 + -4u + 7u2 + (1 + -5u) = 0 Remove parenthesis around (1 + -5u) -2 + -4u + 7u2 + 1 + -5u = 0 Reorder the terms: -2 + 1 + -4u + -5u + 7u2 = 0 Combine like terms: -2 + 1 = -1 -1 + -4u + -5u + 7u2 = 0 Combine like terms: -4u + -5u = -9u -1 + -9u + 7u2 = 0 Solving -1 + -9u + 7u2 = 0 Solving for variable 'u'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.1428571429 + -1.285714286u + u2 = 0 Move the constant term to the right: Add '0.1428571429' to each side of the equation. -0.1428571429 + -1.285714286u + 0.1428571429 + u2 = 0 + 0.1428571429 Reorder the terms: -0.1428571429 + 0.1428571429 + -1.285714286u + u2 = 0 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + -1.285714286u + u2 = 0 + 0.1428571429 -1.285714286u + u2 = 0 + 0.1428571429 Combine like terms: 0 + 0.1428571429 = 0.1428571429 -1.285714286u + u2 = 0.1428571429 The u term is -1.285714286u. Take half its coefficient (-0.642857143). Square it (0.4132653063) and add it to both sides. Add '0.4132653063' to each side of the equation. -1.285714286u + 0.4132653063 + u2 = 0.1428571429 + 0.4132653063 Reorder the terms: 0.4132653063 + -1.285714286u + u2 = 0.1428571429 + 0.4132653063 Combine like terms: 0.1428571429 + 0.4132653063 = 0.5561224492 0.4132653063 + -1.285714286u + u2 = 0.5561224492 Factor a perfect square on the left side: (u + -0.642857143)(u + -0.642857143) = 0.5561224492 Calculate the square root of the right side: 0.745736179 Break this problem into two subproblems by setting (u + -0.642857143) equal to 0.745736179 and -0.745736179.Subproblem 1
u + -0.642857143 = 0.745736179 Simplifying u + -0.642857143 = 0.745736179 Reorder the terms: -0.642857143 + u = 0.745736179 Solving -0.642857143 + u = 0.745736179 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '0.642857143' to each side of the equation. -0.642857143 + 0.642857143 + u = 0.745736179 + 0.642857143 Combine like terms: -0.642857143 + 0.642857143 = 0.000000000 0.000000000 + u = 0.745736179 + 0.642857143 u = 0.745736179 + 0.642857143 Combine like terms: 0.745736179 + 0.642857143 = 1.388593322 u = 1.388593322 Simplifying u = 1.388593322Subproblem 2
u + -0.642857143 = -0.745736179 Simplifying u + -0.642857143 = -0.745736179 Reorder the terms: -0.642857143 + u = -0.745736179 Solving -0.642857143 + u = -0.745736179 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '0.642857143' to each side of the equation. -0.642857143 + 0.642857143 + u = -0.745736179 + 0.642857143 Combine like terms: -0.642857143 + 0.642857143 = 0.000000000 0.000000000 + u = -0.745736179 + 0.642857143 u = -0.745736179 + 0.642857143 Combine like terms: -0.745736179 + 0.642857143 = -0.102879036 u = -0.102879036 Simplifying u = -0.102879036Solution
The solution to the problem is based on the solutions from the subproblems. u = {1.388593322, -0.102879036}
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