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Simplifying u2 + 10u + 25 = 90 Reorder the terms: 25 + 10u + u2 = 90 Solving 25 + 10u + u2 = 90 Solving for variable 'u'. Reorder the terms: 25 + -90 + 10u + u2 = 90 + -90 Combine like terms: 25 + -90 = -65 -65 + 10u + u2 = 90 + -90 Combine like terms: 90 + -90 = 0 -65 + 10u + u2 = 0 Begin completing the square. Move the constant term to the right: Add '65' to each side of the equation. -65 + 10u + 65 + u2 = 0 + 65 Reorder the terms: -65 + 65 + 10u + u2 = 0 + 65 Combine like terms: -65 + 65 = 0 0 + 10u + u2 = 0 + 65 10u + u2 = 0 + 65 Combine like terms: 0 + 65 = 65 10u + u2 = 65 The u term is 10u. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10u + 25 + u2 = 65 + 25 Reorder the terms: 25 + 10u + u2 = 65 + 25 Combine like terms: 65 + 25 = 90 25 + 10u + u2 = 90 Factor a perfect square on the left side: (u + 5)(u + 5) = 90 Calculate the square root of the right side: 9.486832981 Break this problem into two subproblems by setting (u + 5) equal to 9.486832981 and -9.486832981.Subproblem 1
u + 5 = 9.486832981 Simplifying u + 5 = 9.486832981 Reorder the terms: 5 + u = 9.486832981 Solving 5 + u = 9.486832981 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + u = 9.486832981 + -5 Combine like terms: 5 + -5 = 0 0 + u = 9.486832981 + -5 u = 9.486832981 + -5 Combine like terms: 9.486832981 + -5 = 4.486832981 u = 4.486832981 Simplifying u = 4.486832981Subproblem 2
u + 5 = -9.486832981 Simplifying u + 5 = -9.486832981 Reorder the terms: 5 + u = -9.486832981 Solving 5 + u = -9.486832981 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + u = -9.486832981 + -5 Combine like terms: 5 + -5 = 0 0 + u = -9.486832981 + -5 u = -9.486832981 + -5 Combine like terms: -9.486832981 + -5 = -14.486832981 u = -14.486832981 Simplifying u = -14.486832981Solution
The solution to the problem is based on the solutions from the subproblems. u = {4.486832981, -14.486832981}
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