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Simplifying 0 = 4u2 + 20u + -23 Reorder the terms: 0 = -23 + 20u + 4u2 Solving 0 = -23 + 20u + 4u2 Solving for variable 'u'. Combine like terms: 0 + 23 = 23 23 + -20u + -4u2 = -23 + 20u + 4u2 + 23 + -20u + -4u2 Reorder the terms: 23 + -20u + -4u2 = -23 + 23 + 20u + -20u + 4u2 + -4u2 Combine like terms: -23 + 23 = 0 23 + -20u + -4u2 = 0 + 20u + -20u + 4u2 + -4u2 23 + -20u + -4u2 = 20u + -20u + 4u2 + -4u2 Combine like terms: 20u + -20u = 0 23 + -20u + -4u2 = 0 + 4u2 + -4u2 23 + -20u + -4u2 = 4u2 + -4u2 Combine like terms: 4u2 + -4u2 = 0 23 + -20u + -4u2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -5.75 + 5u + u2 = 0 Move the constant term to the right: Add '5.75' to each side of the equation. -5.75 + 5u + 5.75 + u2 = 0 + 5.75 Reorder the terms: -5.75 + 5.75 + 5u + u2 = 0 + 5.75 Combine like terms: -5.75 + 5.75 = 0.00 0.00 + 5u + u2 = 0 + 5.75 5u + u2 = 0 + 5.75 Combine like terms: 0 + 5.75 = 5.75 5u + u2 = 5.75 The u term is 5u. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5u + 6.25 + u2 = 5.75 + 6.25 Reorder the terms: 6.25 + 5u + u2 = 5.75 + 6.25 Combine like terms: 5.75 + 6.25 = 12 6.25 + 5u + u2 = 12 Factor a perfect square on the left side: (u + 2.5)(u + 2.5) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (u + 2.5) equal to 3.464101615 and -3.464101615.Subproblem 1
u + 2.5 = 3.464101615 Simplifying u + 2.5 = 3.464101615 Reorder the terms: 2.5 + u = 3.464101615 Solving 2.5 + u = 3.464101615 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + u = 3.464101615 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + u = 3.464101615 + -2.5 u = 3.464101615 + -2.5 Combine like terms: 3.464101615 + -2.5 = 0.964101615 u = 0.964101615 Simplifying u = 0.964101615Subproblem 2
u + 2.5 = -3.464101615 Simplifying u + 2.5 = -3.464101615 Reorder the terms: 2.5 + u = -3.464101615 Solving 2.5 + u = -3.464101615 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + u = -3.464101615 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + u = -3.464101615 + -2.5 u = -3.464101615 + -2.5 Combine like terms: -3.464101615 + -2.5 = -5.964101615 u = -5.964101615 Simplifying u = -5.964101615Solution
The solution to the problem is based on the solutions from the subproblems. u = {0.964101615, -5.964101615}
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