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Simplifying 2u2 + -7u + -11 = 0 Reorder the terms: -11 + -7u + 2u2 = 0 Solving -11 + -7u + 2u2 = 0 Solving for variable 'u'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -5.5 + -3.5u + u2 = 0 Move the constant term to the right: Add '5.5' to each side of the equation. -5.5 + -3.5u + 5.5 + u2 = 0 + 5.5 Reorder the terms: -5.5 + 5.5 + -3.5u + u2 = 0 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + -3.5u + u2 = 0 + 5.5 -3.5u + u2 = 0 + 5.5 Combine like terms: 0 + 5.5 = 5.5 -3.5u + u2 = 5.5 The u term is -3.5u. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5u + 3.0625 + u2 = 5.5 + 3.0625 Reorder the terms: 3.0625 + -3.5u + u2 = 5.5 + 3.0625 Combine like terms: 5.5 + 3.0625 = 8.5625 3.0625 + -3.5u + u2 = 8.5625 Factor a perfect square on the left side: (u + -1.75)(u + -1.75) = 8.5625 Calculate the square root of the right side: 2.926174978 Break this problem into two subproblems by setting (u + -1.75) equal to 2.926174978 and -2.926174978.Subproblem 1
u + -1.75 = 2.926174978 Simplifying u + -1.75 = 2.926174978 Reorder the terms: -1.75 + u = 2.926174978 Solving -1.75 + u = 2.926174978 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + u = 2.926174978 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + u = 2.926174978 + 1.75 u = 2.926174978 + 1.75 Combine like terms: 2.926174978 + 1.75 = 4.676174978 u = 4.676174978 Simplifying u = 4.676174978Subproblem 2
u + -1.75 = -2.926174978 Simplifying u + -1.75 = -2.926174978 Reorder the terms: -1.75 + u = -2.926174978 Solving -1.75 + u = -2.926174978 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + u = -2.926174978 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + u = -2.926174978 + 1.75 u = -2.926174978 + 1.75 Combine like terms: -2.926174978 + 1.75 = -1.176174978 u = -1.176174978 Simplifying u = -1.176174978Solution
The solution to the problem is based on the solutions from the subproblems. u = {4.676174978, -1.176174978}
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