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Simplifying (u + -3) * 2 = 2u2 + -8u + 1 Reorder the terms: (-3 + u) * 2 = 2u2 + -8u + 1 Reorder the terms for easier multiplication: 2(-3 + u) = 2u2 + -8u + 1 (-3 * 2 + u * 2) = 2u2 + -8u + 1 (-6 + 2u) = 2u2 + -8u + 1 Reorder the terms: -6 + 2u = 1 + -8u + 2u2 Solving -6 + 2u = 1 + -8u + 2u2 Solving for variable 'u'. Reorder the terms: -6 + -1 + 2u + 8u + -2u2 = 1 + -8u + 2u2 + -1 + 8u + -2u2 Combine like terms: -6 + -1 = -7 -7 + 2u + 8u + -2u2 = 1 + -8u + 2u2 + -1 + 8u + -2u2 Combine like terms: 2u + 8u = 10u -7 + 10u + -2u2 = 1 + -8u + 2u2 + -1 + 8u + -2u2 Reorder the terms: -7 + 10u + -2u2 = 1 + -1 + -8u + 8u + 2u2 + -2u2 Combine like terms: 1 + -1 = 0 -7 + 10u + -2u2 = 0 + -8u + 8u + 2u2 + -2u2 -7 + 10u + -2u2 = -8u + 8u + 2u2 + -2u2 Combine like terms: -8u + 8u = 0 -7 + 10u + -2u2 = 0 + 2u2 + -2u2 -7 + 10u + -2u2 = 2u2 + -2u2 Combine like terms: 2u2 + -2u2 = 0 -7 + 10u + -2u2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 3.5 + -5u + u2 = 0 Move the constant term to the right: Add '-3.5' to each side of the equation. 3.5 + -5u + -3.5 + u2 = 0 + -3.5 Reorder the terms: 3.5 + -3.5 + -5u + u2 = 0 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + -5u + u2 = 0 + -3.5 -5u + u2 = 0 + -3.5 Combine like terms: 0 + -3.5 = -3.5 -5u + u2 = -3.5 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 = -3.5 + 6.25 Reorder the terms: 6.25 + -5u + u2 = -3.5 + 6.25 Combine like terms: -3.5 + 6.25 = 2.75 6.25 + -5u + u2 = 2.75 Factor a perfect square on the left side: (u + -2.5)(u + -2.5) = 2.75 Calculate the square root of the right side: 1.658312395 Break this problem into two subproblems by setting (u + -2.5) equal to 1.658312395 and -1.658312395.Subproblem 1
u + -2.5 = 1.658312395 Simplifying u + -2.5 = 1.658312395 Reorder the terms: -2.5 + u = 1.658312395 Solving -2.5 + u = 1.658312395 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 = 1.658312395 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + u = 1.658312395 + 2.5 u = 1.658312395 + 2.5 Combine like terms: 1.658312395 + 2.5 = 4.158312395 u = 4.158312395 Simplifying u = 4.158312395Subproblem 2
u + -2.5 = -1.658312395 Simplifying u + -2.5 = -1.658312395 Reorder the terms: -2.5 + u = -1.658312395 Solving -2.5 + u = -1.658312395 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 = -1.658312395 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + u = -1.658312395 + 2.5 u = -1.658312395 + 2.5 Combine like terms: -1.658312395 + 2.5 = 0.841687605 u = 0.841687605 Simplifying u = 0.841687605Solution
The solution to the problem is based on the solutions from the subproblems. u = {4.158312395, 0.841687605}
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