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Simplifying 2u2 + 9u + -15 = 0 Reorder the terms: -15 + 9u + 2u2 = 0 Solving -15 + 9u + 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'. -7.5 + 4.5u + u2 = 0 Move the constant term to the right: Add '7.5' to each side of the equation. -7.5 + 4.5u + 7.5 + u2 = 0 + 7.5 Reorder the terms: -7.5 + 7.5 + 4.5u + u2 = 0 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + 4.5u + u2 = 0 + 7.5 4.5u + u2 = 0 + 7.5 Combine like terms: 0 + 7.5 = 7.5 4.5u + u2 = 7.5 The u term is 4.5u. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5u + 5.0625 + u2 = 7.5 + 5.0625 Reorder the terms: 5.0625 + 4.5u + u2 = 7.5 + 5.0625 Combine like terms: 7.5 + 5.0625 = 12.5625 5.0625 + 4.5u + u2 = 12.5625 Factor a perfect square on the left side: (u + 2.25)(u + 2.25) = 12.5625 Calculate the square root of the right side: 3.54436172 Break this problem into two subproblems by setting (u + 2.25) equal to 3.54436172 and -3.54436172.Subproblem 1
u + 2.25 = 3.54436172 Simplifying u + 2.25 = 3.54436172 Reorder the terms: 2.25 + u = 3.54436172 Solving 2.25 + u = 3.54436172 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + u = 3.54436172 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + u = 3.54436172 + -2.25 u = 3.54436172 + -2.25 Combine like terms: 3.54436172 + -2.25 = 1.29436172 u = 1.29436172 Simplifying u = 1.29436172Subproblem 2
u + 2.25 = -3.54436172 Simplifying u + 2.25 = -3.54436172 Reorder the terms: 2.25 + u = -3.54436172 Solving 2.25 + u = -3.54436172 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + u = -3.54436172 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + u = -3.54436172 + -2.25 u = -3.54436172 + -2.25 Combine like terms: -3.54436172 + -2.25 = -5.79436172 u = -5.79436172 Simplifying u = -5.79436172Solution
The solution to the problem is based on the solutions from the subproblems. u = {1.29436172, -5.79436172}
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