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Simplifying 14u2 + -11u = 2 Reorder the terms: -11u + 14u2 = 2 Solving -11u + 14u2 = 2 Solving for variable 'u'. Reorder the terms: -2 + -11u + 14u2 = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + -11u + 14u2 = 0 Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -0.1428571429 + -0.7857142857u + u2 = 0 Move the constant term to the right: Add '0.1428571429' to each side of the equation. -0.1428571429 + -0.7857142857u + 0.1428571429 + u2 = 0 + 0.1428571429 Reorder the terms: -0.1428571429 + 0.1428571429 + -0.7857142857u + u2 = 0 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + -0.7857142857u + u2 = 0 + 0.1428571429 -0.7857142857u + u2 = 0 + 0.1428571429 Combine like terms: 0 + 0.1428571429 = 0.1428571429 -0.7857142857u + u2 = 0.1428571429 The u term is -0.7857142857u. Take half its coefficient (-0.3928571429). Square it (0.1543367347) and add it to both sides. Add '0.1543367347' to each side of the equation. -0.7857142857u + 0.1543367347 + u2 = 0.1428571429 + 0.1543367347 Reorder the terms: 0.1543367347 + -0.7857142857u + u2 = 0.1428571429 + 0.1543367347 Combine like terms: 0.1428571429 + 0.1543367347 = 0.2971938776 0.1543367347 + -0.7857142857u + u2 = 0.2971938776 Factor a perfect square on the left side: (u + -0.3928571429)(u + -0.3928571429) = 0.2971938776 Calculate the square root of the right side: 0.545154912 Break this problem into two subproblems by setting (u + -0.3928571429) equal to 0.545154912 and -0.545154912.Subproblem 1
u + -0.3928571429 = 0.545154912 Simplifying u + -0.3928571429 = 0.545154912 Reorder the terms: -0.3928571429 + u = 0.545154912 Solving -0.3928571429 + u = 0.545154912 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '0.3928571429' to each side of the equation. -0.3928571429 + 0.3928571429 + u = 0.545154912 + 0.3928571429 Combine like terms: -0.3928571429 + 0.3928571429 = 0.0000000000 0.0000000000 + u = 0.545154912 + 0.3928571429 u = 0.545154912 + 0.3928571429 Combine like terms: 0.545154912 + 0.3928571429 = 0.9380120549 u = 0.9380120549 Simplifying u = 0.9380120549Subproblem 2
u + -0.3928571429 = -0.545154912 Simplifying u + -0.3928571429 = -0.545154912 Reorder the terms: -0.3928571429 + u = -0.545154912 Solving -0.3928571429 + u = -0.545154912 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '0.3928571429' to each side of the equation. -0.3928571429 + 0.3928571429 + u = -0.545154912 + 0.3928571429 Combine like terms: -0.3928571429 + 0.3928571429 = 0.0000000000 0.0000000000 + u = -0.545154912 + 0.3928571429 u = -0.545154912 + 0.3928571429 Combine like terms: -0.545154912 + 0.3928571429 = -0.1522977691 u = -0.1522977691 Simplifying u = -0.1522977691Solution
The solution to the problem is based on the solutions from the subproblems. u = {0.9380120549, -0.1522977691}
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