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Simplifying -9u2 + 12u + 20 = 0 Reorder the terms: 20 + 12u + -9u2 = 0 Solving 20 + 12u + -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'. -2.222222222 + -1.333333333u + u2 = 0 Move the constant term to the right: Add '2.222222222' to each side of the equation. -2.222222222 + -1.333333333u + 2.222222222 + u2 = 0 + 2.222222222 Reorder the terms: -2.222222222 + 2.222222222 + -1.333333333u + u2 = 0 + 2.222222222 Combine like terms: -2.222222222 + 2.222222222 = 0.000000000 0.000000000 + -1.333333333u + u2 = 0 + 2.222222222 -1.333333333u + u2 = 0 + 2.222222222 Combine like terms: 0 + 2.222222222 = 2.222222222 -1.333333333u + u2 = 2.222222222 The u term is -1.333333333u. Take half its coefficient (-0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. -1.333333333u + 0.4444444442 + u2 = 2.222222222 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333u + u2 = 2.222222222 + 0.4444444442 Combine like terms: 2.222222222 + 0.4444444442 = 2.6666666662 0.4444444442 + -1.333333333u + u2 = 2.6666666662 Factor a perfect square on the left side: (u + -0.6666666665)(u + -0.6666666665) = 2.6666666662 Calculate the square root of the right side: 1.632993162 Break this problem into two subproblems by setting (u + -0.6666666665) equal to 1.632993162 and -1.632993162.Subproblem 1
u + -0.6666666665 = 1.632993162 Simplifying u + -0.6666666665 = 1.632993162 Reorder the terms: -0.6666666665 + u = 1.632993162 Solving -0.6666666665 + u = 1.632993162 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + u = 1.632993162 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + u = 1.632993162 + 0.6666666665 u = 1.632993162 + 0.6666666665 Combine like terms: 1.632993162 + 0.6666666665 = 2.2996598285 u = 2.2996598285 Simplifying u = 2.2996598285Subproblem 2
u + -0.6666666665 = -1.632993162 Simplifying u + -0.6666666665 = -1.632993162 Reorder the terms: -0.6666666665 + u = -1.632993162 Solving -0.6666666665 + u = -1.632993162 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + u = -1.632993162 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + u = -1.632993162 + 0.6666666665 u = -1.632993162 + 0.6666666665 Combine like terms: -1.632993162 + 0.6666666665 = -0.9663264955 u = -0.9663264955 Simplifying u = -0.9663264955Solution
The solution to the problem is based on the solutions from the subproblems. u = {2.2996598285, -0.9663264955}
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