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Simplifying -2u2 + 5 = 3u2 + -10u Reorder the terms: 5 + -2u2 = 3u2 + -10u Reorder the terms: 5 + -2u2 = -10u + 3u2 Solving 5 + -2u2 = -10u + 3u2 Solving for variable 'u'. Reorder the terms: 5 + 10u + -2u2 + -3u2 = -10u + 3u2 + 10u + -3u2 Combine like terms: -2u2 + -3u2 = -5u2 5 + 10u + -5u2 = -10u + 3u2 + 10u + -3u2 Reorder the terms: 5 + 10u + -5u2 = -10u + 10u + 3u2 + -3u2 Combine like terms: -10u + 10u = 0 5 + 10u + -5u2 = 0 + 3u2 + -3u2 5 + 10u + -5u2 = 3u2 + -3u2 Combine like terms: 3u2 + -3u2 = 0 5 + 10u + -5u2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(1 + 2u + -1u2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(1 + 2u + -1u2)' equal to zero and attempt to solve: Simplifying 1 + 2u + -1u2 = 0 Solving 1 + 2u + -1u2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1 + -2u + u2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -2u + 1 + u2 = 0 + 1 Reorder the terms: -1 + 1 + -2u + u2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2u + u2 = 0 + 1 -2u + u2 = 0 + 1 Combine like terms: 0 + 1 = 1 -2u + u2 = 1 The u term is -2u. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2u + 1 + u2 = 1 + 1 Reorder the terms: 1 + -2u + u2 = 1 + 1 Combine like terms: 1 + 1 = 2 1 + -2u + u2 = 2 Factor a perfect square on the left side: (u + -1)(u + -1) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (u + -1) equal to 1.414213562 and -1.414213562.Subproblem 1
u + -1 = 1.414213562 Simplifying u + -1 = 1.414213562 Reorder the terms: -1 + u = 1.414213562 Solving -1 + u = 1.414213562 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + u = 1.414213562 + 1 Combine like terms: -1 + 1 = 0 0 + u = 1.414213562 + 1 u = 1.414213562 + 1 Combine like terms: 1.414213562 + 1 = 2.414213562 u = 2.414213562 Simplifying u = 2.414213562Subproblem 2
u + -1 = -1.414213562 Simplifying u + -1 = -1.414213562 Reorder the terms: -1 + u = -1.414213562 Solving -1 + u = -1.414213562 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + u = -1.414213562 + 1 Combine like terms: -1 + 1 = 0 0 + u = -1.414213562 + 1 u = -1.414213562 + 1 Combine like terms: -1.414213562 + 1 = -0.414213562 u = -0.414213562 Simplifying u = -0.414213562Solution
The solution to the problem is based on the solutions from the subproblems. u = {2.414213562, -0.414213562}Solution
u = {2.414213562, -0.414213562}
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