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Simplifying u2 + -10.5u + 13.5 = 0 Reorder the terms: 13.5 + -10.5u + u2 = 0 Solving 13.5 + -10.5u + u2 = 0 Solving for variable 'u'. Begin completing the square. Move the constant term to the right: Add '-13.5' to each side of the equation. 13.5 + -10.5u + -13.5 + u2 = 0 + -13.5 Reorder the terms: 13.5 + -13.5 + -10.5u + u2 = 0 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + -10.5u + u2 = 0 + -13.5 -10.5u + u2 = 0 + -13.5 Combine like terms: 0 + -13.5 = -13.5 -10.5u + u2 = -13.5 The u term is -10.5u. Take half its coefficient (-5.25). Square it (27.5625) and add it to both sides. Add '27.5625' to each side of the equation. -10.5u + 27.5625 + u2 = -13.5 + 27.5625 Reorder the terms: 27.5625 + -10.5u + u2 = -13.5 + 27.5625 Combine like terms: -13.5 + 27.5625 = 14.0625 27.5625 + -10.5u + u2 = 14.0625 Factor a perfect square on the left side: (u + -5.25)(u + -5.25) = 14.0625 Calculate the square root of the right side: 3.75 Break this problem into two subproblems by setting (u + -5.25) equal to 3.75 and -3.75.Subproblem 1
u + -5.25 = 3.75 Simplifying u + -5.25 = 3.75 Reorder the terms: -5.25 + u = 3.75 Solving -5.25 + u = 3.75 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '5.25' to each side of the equation. -5.25 + 5.25 + u = 3.75 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + u = 3.75 + 5.25 u = 3.75 + 5.25 Combine like terms: 3.75 + 5.25 = 9 u = 9 Simplifying u = 9Subproblem 2
u + -5.25 = -3.75 Simplifying u + -5.25 = -3.75 Reorder the terms: -5.25 + u = -3.75 Solving -5.25 + u = -3.75 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '5.25' to each side of the equation. -5.25 + 5.25 + u = -3.75 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + u = -3.75 + 5.25 u = -3.75 + 5.25 Combine like terms: -3.75 + 5.25 = 1.5 u = 1.5 Simplifying u = 1.5Solution
The solution to the problem is based on the solutions from the subproblems. u = {9, 1.5}
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