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Simplifying -4u2 + 9u + -3 = 0 Reorder the terms: -3 + 9u + -4u2 = 0 Solving -3 + 9u + -4u2 = 0 Solving for variable 'u'. Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 0.75 + -2.25u + u2 = 0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + -2.25u + -0.75 + u2 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + -2.25u + u2 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + -2.25u + u2 = 0 + -0.75 -2.25u + u2 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 -2.25u + u2 = -0.75 The u term is -2.25u. Take half its coefficient (-1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. -2.25u + 1.265625 + u2 = -0.75 + 1.265625 Reorder the terms: 1.265625 + -2.25u + u2 = -0.75 + 1.265625 Combine like terms: -0.75 + 1.265625 = 0.515625 1.265625 + -2.25u + u2 = 0.515625 Factor a perfect square on the left side: (u + -1.125)(u + -1.125) = 0.515625 Calculate the square root of the right side: 0.718070331 Break this problem into two subproblems by setting (u + -1.125) equal to 0.718070331 and -0.718070331.Subproblem 1
u + -1.125 = 0.718070331 Simplifying u + -1.125 = 0.718070331 Reorder the terms: -1.125 + u = 0.718070331 Solving -1.125 + u = 0.718070331 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + u = 0.718070331 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + u = 0.718070331 + 1.125 u = 0.718070331 + 1.125 Combine like terms: 0.718070331 + 1.125 = 1.843070331 u = 1.843070331 Simplifying u = 1.843070331Subproblem 2
u + -1.125 = -0.718070331 Simplifying u + -1.125 = -0.718070331 Reorder the terms: -1.125 + u = -0.718070331 Solving -1.125 + u = -0.718070331 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + u = -0.718070331 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + u = -0.718070331 + 1.125 u = -0.718070331 + 1.125 Combine like terms: -0.718070331 + 1.125 = 0.406929669 u = 0.406929669 Simplifying u = 0.406929669Solution
The solution to the problem is based on the solutions from the subproblems. u = {1.843070331, 0.406929669}
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