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Simplifying -1u2 + 25u + -30 = 0 Reorder the terms: -30 + 25u + -1u2 = 0 Solving -30 + 25u + -1u2 = 0 Solving for variable 'u'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 30 + -25u + u2 = 0 Move the constant term to the right: Add '-30' to each side of the equation. 30 + -25u + -30 + u2 = 0 + -30 Reorder the terms: 30 + -30 + -25u + u2 = 0 + -30 Combine like terms: 30 + -30 = 0 0 + -25u + u2 = 0 + -30 -25u + u2 = 0 + -30 Combine like terms: 0 + -30 = -30 -25u + u2 = -30 The u term is -25u. Take half its coefficient (-12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. -25u + 156.25 + u2 = -30 + 156.25 Reorder the terms: 156.25 + -25u + u2 = -30 + 156.25 Combine like terms: -30 + 156.25 = 126.25 156.25 + -25u + u2 = 126.25 Factor a perfect square on the left side: (u + -12.5)(u + -12.5) = 126.25 Calculate the square root of the right side: 11.236102527 Break this problem into two subproblems by setting (u + -12.5) equal to 11.236102527 and -11.236102527.Subproblem 1
u + -12.5 = 11.236102527 Simplifying u + -12.5 = 11.236102527 Reorder the terms: -12.5 + u = 11.236102527 Solving -12.5 + u = 11.236102527 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + u = 11.236102527 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + u = 11.236102527 + 12.5 u = 11.236102527 + 12.5 Combine like terms: 11.236102527 + 12.5 = 23.736102527 u = 23.736102527 Simplifying u = 23.736102527Subproblem 2
u + -12.5 = -11.236102527 Simplifying u + -12.5 = -11.236102527 Reorder the terms: -12.5 + u = -11.236102527 Solving -12.5 + u = -11.236102527 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + u = -11.236102527 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + u = -11.236102527 + 12.5 u = -11.236102527 + 12.5 Combine like terms: -11.236102527 + 12.5 = 1.263897473 u = 1.263897473 Simplifying u = 1.263897473Solution
The solution to the problem is based on the solutions from the subproblems. u = {23.736102527, 1.263897473}
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