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Simplifying (5u2 + -1u + -7) + (6u2 + -2u + 3) = 0 Reorder the terms: (-7 + -1u + 5u2) + (6u2 + -2u + 3) = 0 Remove parenthesis around (-7 + -1u + 5u2) -7 + -1u + 5u2 + (6u2 + -2u + 3) = 0 Reorder the terms: -7 + -1u + 5u2 + (3 + -2u + 6u2) = 0 Remove parenthesis around (3 + -2u + 6u2) -7 + -1u + 5u2 + 3 + -2u + 6u2 = 0 Reorder the terms: -7 + 3 + -1u + -2u + 5u2 + 6u2 = 0 Combine like terms: -7 + 3 = -4 -4 + -1u + -2u + 5u2 + 6u2 = 0 Combine like terms: -1u + -2u = -3u -4 + -3u + 5u2 + 6u2 = 0 Combine like terms: 5u2 + 6u2 = 11u2 -4 + -3u + 11u2 = 0 Solving -4 + -3u + 11u2 = 0 Solving for variable 'u'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -0.3636363636 + -0.2727272727u + u2 = 0 Move the constant term to the right: Add '0.3636363636' to each side of the equation. -0.3636363636 + -0.2727272727u + 0.3636363636 + u2 = 0 + 0.3636363636 Reorder the terms: -0.3636363636 + 0.3636363636 + -0.2727272727u + u2 = 0 + 0.3636363636 Combine like terms: -0.3636363636 + 0.3636363636 = 0.0000000000 0.0000000000 + -0.2727272727u + u2 = 0 + 0.3636363636 -0.2727272727u + u2 = 0 + 0.3636363636 Combine like terms: 0 + 0.3636363636 = 0.3636363636 -0.2727272727u + u2 = 0.3636363636 The u term is -0.2727272727u. Take half its coefficient (-0.1363636364). Square it (0.01859504133) and add it to both sides. Add '0.01859504133' to each side of the equation. -0.2727272727u + 0.01859504133 + u2 = 0.3636363636 + 0.01859504133 Reorder the terms: 0.01859504133 + -0.2727272727u + u2 = 0.3636363636 + 0.01859504133 Combine like terms: 0.3636363636 + 0.01859504133 = 0.38223140493 0.01859504133 + -0.2727272727u + u2 = 0.38223140493 Factor a perfect square on the left side: (u + -0.1363636364)(u + -0.1363636364) = 0.38223140493 Calculate the square root of the right side: 0.618248659 Break this problem into two subproblems by setting (u + -0.1363636364) equal to 0.618248659 and -0.618248659.Subproblem 1
u + -0.1363636364 = 0.618248659 Simplifying u + -0.1363636364 = 0.618248659 Reorder the terms: -0.1363636364 + u = 0.618248659 Solving -0.1363636364 + u = 0.618248659 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '0.1363636364' to each side of the equation. -0.1363636364 + 0.1363636364 + u = 0.618248659 + 0.1363636364 Combine like terms: -0.1363636364 + 0.1363636364 = 0.0000000000 0.0000000000 + u = 0.618248659 + 0.1363636364 u = 0.618248659 + 0.1363636364 Combine like terms: 0.618248659 + 0.1363636364 = 0.7546122954 u = 0.7546122954 Simplifying u = 0.7546122954Subproblem 2
u + -0.1363636364 = -0.618248659 Simplifying u + -0.1363636364 = -0.618248659 Reorder the terms: -0.1363636364 + u = -0.618248659 Solving -0.1363636364 + u = -0.618248659 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '0.1363636364' to each side of the equation. -0.1363636364 + 0.1363636364 + u = -0.618248659 + 0.1363636364 Combine like terms: -0.1363636364 + 0.1363636364 = 0.0000000000 0.0000000000 + u = -0.618248659 + 0.1363636364 u = -0.618248659 + 0.1363636364 Combine like terms: -0.618248659 + 0.1363636364 = -0.4818850226 u = -0.4818850226 Simplifying u = -0.4818850226Solution
The solution to the problem is based on the solutions from the subproblems. u = {0.7546122954, -0.4818850226}
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