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Simplifying 5u2 + -29u + -5 = 0 Reorder the terms: -5 + -29u + 5u2 = 0 Solving -5 + -29u + 5u2 = 0 Solving for variable 'u'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1 + -5.8u + u2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -5.8u + 1 + u2 = 0 + 1 Reorder the terms: -1 + 1 + -5.8u + u2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -5.8u + u2 = 0 + 1 -5.8u + u2 = 0 + 1 Combine like terms: 0 + 1 = 1 -5.8u + u2 = 1 The u term is -5.8u. Take half its coefficient (-2.9). Square it (8.41) and add it to both sides. Add '8.41' to each side of the equation. -5.8u + 8.41 + u2 = 1 + 8.41 Reorder the terms: 8.41 + -5.8u + u2 = 1 + 8.41 Combine like terms: 1 + 8.41 = 9.41 8.41 + -5.8u + u2 = 9.41 Factor a perfect square on the left side: (u + -2.9)(u + -2.9) = 9.41 Calculate the square root of the right side: 3.06757233 Break this problem into two subproblems by setting (u + -2.9) equal to 3.06757233 and -3.06757233.Subproblem 1
u + -2.9 = 3.06757233 Simplifying u + -2.9 = 3.06757233 Reorder the terms: -2.9 + u = 3.06757233 Solving -2.9 + u = 3.06757233 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '2.9' to each side of the equation. -2.9 + 2.9 + u = 3.06757233 + 2.9 Combine like terms: -2.9 + 2.9 = 0.0 0.0 + u = 3.06757233 + 2.9 u = 3.06757233 + 2.9 Combine like terms: 3.06757233 + 2.9 = 5.96757233 u = 5.96757233 Simplifying u = 5.96757233Subproblem 2
u + -2.9 = -3.06757233 Simplifying u + -2.9 = -3.06757233 Reorder the terms: -2.9 + u = -3.06757233 Solving -2.9 + u = -3.06757233 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '2.9' to each side of the equation. -2.9 + 2.9 + u = -3.06757233 + 2.9 Combine like terms: -2.9 + 2.9 = 0.0 0.0 + u = -3.06757233 + 2.9 u = -3.06757233 + 2.9 Combine like terms: -3.06757233 + 2.9 = -0.16757233 u = -0.16757233 Simplifying u = -0.16757233Solution
The solution to the problem is based on the solutions from the subproblems. u = {5.96757233, -0.16757233}
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