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Simplifying 9u2 + 24u + -7 = 0 Reorder the terms: -7 + 24u + 9u2 = 0 Solving -7 + 24u + 9u2 = 0 Solving for variable 'u'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.7777777778 + 2.666666667u + u2 = 0 Move the constant term to the right: Add '0.7777777778' to each side of the equation. -0.7777777778 + 2.666666667u + 0.7777777778 + u2 = 0 + 0.7777777778 Reorder the terms: -0.7777777778 + 0.7777777778 + 2.666666667u + u2 = 0 + 0.7777777778 Combine like terms: -0.7777777778 + 0.7777777778 = 0.0000000000 0.0000000000 + 2.666666667u + u2 = 0 + 0.7777777778 2.666666667u + u2 = 0 + 0.7777777778 Combine like terms: 0 + 0.7777777778 = 0.7777777778 2.666666667u + u2 = 0.7777777778 The u term is 2.666666667u. Take half its coefficient (1.333333334). Square it (1.777777780) and add it to both sides. Add '1.777777780' to each side of the equation. 2.666666667u + 1.777777780 + u2 = 0.7777777778 + 1.777777780 Reorder the terms: 1.777777780 + 2.666666667u + u2 = 0.7777777778 + 1.777777780 Combine like terms: 0.7777777778 + 1.777777780 = 2.5555555578 1.777777780 + 2.666666667u + u2 = 2.5555555578 Factor a perfect square on the left side: (u + 1.333333334)(u + 1.333333334) = 2.5555555578 Calculate the square root of the right side: 1.598610508 Break this problem into two subproblems by setting (u + 1.333333334) equal to 1.598610508 and -1.598610508.Subproblem 1
u + 1.333333334 = 1.598610508 Simplifying u + 1.333333334 = 1.598610508 Reorder the terms: 1.333333334 + u = 1.598610508 Solving 1.333333334 + u = 1.598610508 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + u = 1.598610508 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + u = 1.598610508 + -1.333333334 u = 1.598610508 + -1.333333334 Combine like terms: 1.598610508 + -1.333333334 = 0.265277174 u = 0.265277174 Simplifying u = 0.265277174Subproblem 2
u + 1.333333334 = -1.598610508 Simplifying u + 1.333333334 = -1.598610508 Reorder the terms: 1.333333334 + u = -1.598610508 Solving 1.333333334 + u = -1.598610508 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + u = -1.598610508 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + u = -1.598610508 + -1.333333334 u = -1.598610508 + -1.333333334 Combine like terms: -1.598610508 + -1.333333334 = -2.931943842 u = -2.931943842 Simplifying u = -2.931943842Solution
The solution to the problem is based on the solutions from the subproblems. u = {0.265277174, -2.931943842}
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