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Simplifying 2u2 + 25u + 8 = 0 Reorder the terms: 8 + 25u + 2u2 = 0 Solving 8 + 25u + 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'. 4 + 12.5u + u2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + 12.5u + -4 + u2 = 0 + -4 Reorder the terms: 4 + -4 + 12.5u + u2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 12.5u + u2 = 0 + -4 12.5u + u2 = 0 + -4 Combine like terms: 0 + -4 = -4 12.5u + u2 = -4 The u term is 12.5u. Take half its coefficient (6.25). Square it (39.0625) and add it to both sides. Add '39.0625' to each side of the equation. 12.5u + 39.0625 + u2 = -4 + 39.0625 Reorder the terms: 39.0625 + 12.5u + u2 = -4 + 39.0625 Combine like terms: -4 + 39.0625 = 35.0625 39.0625 + 12.5u + u2 = 35.0625 Factor a perfect square on the left side: (u + 6.25)(u + 6.25) = 35.0625 Calculate the square root of the right side: 5.921359641 Break this problem into two subproblems by setting (u + 6.25) equal to 5.921359641 and -5.921359641.Subproblem 1
u + 6.25 = 5.921359641 Simplifying u + 6.25 = 5.921359641 Reorder the terms: 6.25 + u = 5.921359641 Solving 6.25 + u = 5.921359641 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-6.25' to each side of the equation. 6.25 + -6.25 + u = 5.921359641 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + u = 5.921359641 + -6.25 u = 5.921359641 + -6.25 Combine like terms: 5.921359641 + -6.25 = -0.328640359 u = -0.328640359 Simplifying u = -0.328640359Subproblem 2
u + 6.25 = -5.921359641 Simplifying u + 6.25 = -5.921359641 Reorder the terms: 6.25 + u = -5.921359641 Solving 6.25 + u = -5.921359641 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-6.25' to each side of the equation. 6.25 + -6.25 + u = -5.921359641 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + u = -5.921359641 + -6.25 u = -5.921359641 + -6.25 Combine like terms: -5.921359641 + -6.25 = -12.171359641 u = -12.171359641 Simplifying u = -12.171359641Solution
The solution to the problem is based on the solutions from the subproblems. u = {-0.328640359, -12.171359641}
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