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Simplifying (u + -2)(u + -2) = 2u2 + 2 + -1u Reorder the terms: (-2 + u)(u + -2) = 2u2 + 2 + -1u Reorder the terms: (-2 + u)(-2 + u) = 2u2 + 2 + -1u Multiply (-2 + u) * (-2 + u) (-2(-2 + u) + u(-2 + u)) = 2u2 + 2 + -1u ((-2 * -2 + u * -2) + u(-2 + u)) = 2u2 + 2 + -1u ((4 + -2u) + u(-2 + u)) = 2u2 + 2 + -1u (4 + -2u + (-2 * u + u * u)) = 2u2 + 2 + -1u (4 + -2u + (-2u + u2)) = 2u2 + 2 + -1u Combine like terms: -2u + -2u = -4u (4 + -4u + u2) = 2u2 + 2 + -1u Reorder the terms: 4 + -4u + u2 = 2 + -1u + 2u2 Solving 4 + -4u + u2 = 2 + -1u + 2u2 Solving for variable 'u'. Reorder the terms: 4 + -2 + -4u + u + u2 + -2u2 = 2 + -1u + 2u2 + -2 + u + -2u2 Combine like terms: 4 + -2 = 2 2 + -4u + u + u2 + -2u2 = 2 + -1u + 2u2 + -2 + u + -2u2 Combine like terms: -4u + u = -3u 2 + -3u + u2 + -2u2 = 2 + -1u + 2u2 + -2 + u + -2u2 Combine like terms: u2 + -2u2 = -1u2 2 + -3u + -1u2 = 2 + -1u + 2u2 + -2 + u + -2u2 Reorder the terms: 2 + -3u + -1u2 = 2 + -2 + -1u + u + 2u2 + -2u2 Combine like terms: 2 + -2 = 0 2 + -3u + -1u2 = 0 + -1u + u + 2u2 + -2u2 2 + -3u + -1u2 = -1u + u + 2u2 + -2u2 Combine like terms: -1u + u = 0 2 + -3u + -1u2 = 0 + 2u2 + -2u2 2 + -3u + -1u2 = 2u2 + -2u2 Combine like terms: 2u2 + -2u2 = 0 2 + -3u + -1u2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -2 + 3u + u2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 3u + 2 + u2 = 0 + 2 Reorder the terms: -2 + 2 + 3u + u2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 3u + u2 = 0 + 2 3u + u2 = 0 + 2 Combine like terms: 0 + 2 = 2 3u + u2 = 2 The u term is 3u. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3u + 2.25 + u2 = 2 + 2.25 Reorder the terms: 2.25 + 3u + u2 = 2 + 2.25 Combine like terms: 2 + 2.25 = 4.25 2.25 + 3u + u2 = 4.25 Factor a perfect square on the left side: (u + 1.5)(u + 1.5) = 4.25 Calculate the square root of the right side: 2.061552813 Break this problem into two subproblems by setting (u + 1.5) equal to 2.061552813 and -2.061552813.Subproblem 1
u + 1.5 = 2.061552813 Simplifying u + 1.5 = 2.061552813 Reorder the terms: 1.5 + u = 2.061552813 Solving 1.5 + u = 2.061552813 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + u = 2.061552813 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + u = 2.061552813 + -1.5 u = 2.061552813 + -1.5 Combine like terms: 2.061552813 + -1.5 = 0.561552813 u = 0.561552813 Simplifying u = 0.561552813Subproblem 2
u + 1.5 = -2.061552813 Simplifying u + 1.5 = -2.061552813 Reorder the terms: 1.5 + u = -2.061552813 Solving 1.5 + u = -2.061552813 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + u = -2.061552813 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + u = -2.061552813 + -1.5 u = -2.061552813 + -1.5 Combine like terms: -2.061552813 + -1.5 = -3.561552813 u = -3.561552813 Simplifying u = -3.561552813Solution
The solution to the problem is based on the solutions from the subproblems. u = {0.561552813, -3.561552813}
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