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Simplifying -1u = 7u2 + -7 Reorder the terms: -1u = -7 + 7u2 Solving -1u = -7 + 7u2 Solving for variable 'u'. Reorder the terms: 7 + -1u + -7u2 = -7 + 7u2 + 7 + -7u2 Reorder the terms: 7 + -1u + -7u2 = -7 + 7 + 7u2 + -7u2 Combine like terms: -7 + 7 = 0 7 + -1u + -7u2 = 0 + 7u2 + -7u2 7 + -1u + -7u2 = 7u2 + -7u2 Combine like terms: 7u2 + -7u2 = 0 7 + -1u + -7u2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -1 + 0.1428571429u + u2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 0.1428571429u + 1 + u2 = 0 + 1 Reorder the terms: -1 + 1 + 0.1428571429u + u2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 0.1428571429u + u2 = 0 + 1 0.1428571429u + u2 = 0 + 1 Combine like terms: 0 + 1 = 1 0.1428571429u + u2 = 1 The u term is 0.1428571429u. Take half its coefficient (0.07142857145). Square it (0.005102040819) and add it to both sides. Add '0.005102040819' to each side of the equation. 0.1428571429u + 0.005102040819 + u2 = 1 + 0.005102040819 Reorder the terms: 0.005102040819 + 0.1428571429u + u2 = 1 + 0.005102040819 Combine like terms: 1 + 0.005102040819 = 1.005102040819 0.005102040819 + 0.1428571429u + u2 = 1.005102040819 Factor a perfect square on the left side: (u + 0.07142857145)(u + 0.07142857145) = 1.005102040819 Calculate the square root of the right side: 1.002547775 Break this problem into two subproblems by setting (u + 0.07142857145) equal to 1.002547775 and -1.002547775.Subproblem 1
u + 0.07142857145 = 1.002547775 Simplifying u + 0.07142857145 = 1.002547775 Reorder the terms: 0.07142857145 + u = 1.002547775 Solving 0.07142857145 + u = 1.002547775 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-0.07142857145' to each side of the equation. 0.07142857145 + -0.07142857145 + u = 1.002547775 + -0.07142857145 Combine like terms: 0.07142857145 + -0.07142857145 = 0.00000000000 0.00000000000 + u = 1.002547775 + -0.07142857145 u = 1.002547775 + -0.07142857145 Combine like terms: 1.002547775 + -0.07142857145 = 0.93111920355 u = 0.93111920355 Simplifying u = 0.93111920355Subproblem 2
u + 0.07142857145 = -1.002547775 Simplifying u + 0.07142857145 = -1.002547775 Reorder the terms: 0.07142857145 + u = -1.002547775 Solving 0.07142857145 + u = -1.002547775 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-0.07142857145' to each side of the equation. 0.07142857145 + -0.07142857145 + u = -1.002547775 + -0.07142857145 Combine like terms: 0.07142857145 + -0.07142857145 = 0.00000000000 0.00000000000 + u = -1.002547775 + -0.07142857145 u = -1.002547775 + -0.07142857145 Combine like terms: -1.002547775 + -0.07142857145 = -1.07397634645 u = -1.07397634645 Simplifying u = -1.07397634645Solution
The solution to the problem is based on the solutions from the subproblems. u = {0.93111920355, -1.07397634645}
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