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Simplifying 7u2 + -12u + 4 = 0 Reorder the terms: 4 + -12u + 7u2 = 0 Solving 4 + -12u + 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'. 0.5714285714 + -1.714285714u + u2 = 0 Move the constant term to the right: Add '-0.5714285714' to each side of the equation. 0.5714285714 + -1.714285714u + -0.5714285714 + u2 = 0 + -0.5714285714 Reorder the terms: 0.5714285714 + -0.5714285714 + -1.714285714u + u2 = 0 + -0.5714285714 Combine like terms: 0.5714285714 + -0.5714285714 = 0.0000000000 0.0000000000 + -1.714285714u + u2 = 0 + -0.5714285714 -1.714285714u + u2 = 0 + -0.5714285714 Combine like terms: 0 + -0.5714285714 = -0.5714285714 -1.714285714u + u2 = -0.5714285714 The u term is -1.714285714u. Take half its coefficient (-0.857142857). Square it (0.7346938773) and add it to both sides. Add '0.7346938773' to each side of the equation. -1.714285714u + 0.7346938773 + u2 = -0.5714285714 + 0.7346938773 Reorder the terms: 0.7346938773 + -1.714285714u + u2 = -0.5714285714 + 0.7346938773 Combine like terms: -0.5714285714 + 0.7346938773 = 0.1632653059 0.7346938773 + -1.714285714u + u2 = 0.1632653059 Factor a perfect square on the left side: (u + -0.857142857)(u + -0.857142857) = 0.1632653059 Calculate the square root of the right side: 0.404061018 Break this problem into two subproblems by setting (u + -0.857142857) equal to 0.404061018 and -0.404061018.Subproblem 1
u + -0.857142857 = 0.404061018 Simplifying u + -0.857142857 = 0.404061018 Reorder the terms: -0.857142857 + u = 0.404061018 Solving -0.857142857 + u = 0.404061018 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '0.857142857' to each side of the equation. -0.857142857 + 0.857142857 + u = 0.404061018 + 0.857142857 Combine like terms: -0.857142857 + 0.857142857 = 0.000000000 0.000000000 + u = 0.404061018 + 0.857142857 u = 0.404061018 + 0.857142857 Combine like terms: 0.404061018 + 0.857142857 = 1.261203875 u = 1.261203875 Simplifying u = 1.261203875Subproblem 2
u + -0.857142857 = -0.404061018 Simplifying u + -0.857142857 = -0.404061018 Reorder the terms: -0.857142857 + u = -0.404061018 Solving -0.857142857 + u = -0.404061018 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '0.857142857' to each side of the equation. -0.857142857 + 0.857142857 + u = -0.404061018 + 0.857142857 Combine like terms: -0.857142857 + 0.857142857 = 0.000000000 0.000000000 + u = -0.404061018 + 0.857142857 u = -0.404061018 + 0.857142857 Combine like terms: -0.404061018 + 0.857142857 = 0.453081839 u = 0.453081839 Simplifying u = 0.453081839Solution
The solution to the problem is based on the solutions from the subproblems. u = {1.261203875, 0.453081839}
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