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Simplifying u + 6 = (u2) + 7u + 10 Reorder the terms: 6 + u = (u2) + 7u + 10 6 + u = u2 + 7u + 10 Reorder the terms: 6 + u = 10 + 7u + u2 Solving 6 + u = 10 + 7u + u2 Solving for variable 'u'. Reorder the terms: 6 + -10 + u + -7u + -1u2 = 10 + 7u + u2 + -10 + -7u + -1u2 Combine like terms: 6 + -10 = -4 -4 + u + -7u + -1u2 = 10 + 7u + u2 + -10 + -7u + -1u2 Combine like terms: u + -7u = -6u -4 + -6u + -1u2 = 10 + 7u + u2 + -10 + -7u + -1u2 Reorder the terms: -4 + -6u + -1u2 = 10 + -10 + 7u + -7u + u2 + -1u2 Combine like terms: 10 + -10 = 0 -4 + -6u + -1u2 = 0 + 7u + -7u + u2 + -1u2 -4 + -6u + -1u2 = 7u + -7u + u2 + -1u2 Combine like terms: 7u + -7u = 0 -4 + -6u + -1u2 = 0 + u2 + -1u2 -4 + -6u + -1u2 = u2 + -1u2 Combine like terms: u2 + -1u2 = 0 -4 + -6u + -1u2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(4 + 6u + u2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(4 + 6u + u2)' equal to zero and attempt to solve: Simplifying 4 + 6u + u2 = 0 Solving 4 + 6u + u2 = 0 Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + 6u + -4 + u2 = 0 + -4 Reorder the terms: 4 + -4 + 6u + u2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 6u + u2 = 0 + -4 6u + u2 = 0 + -4 Combine like terms: 0 + -4 = -4 6u + u2 = -4 The u term is 6u. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6u + 9 + u2 = -4 + 9 Reorder the terms: 9 + 6u + u2 = -4 + 9 Combine like terms: -4 + 9 = 5 9 + 6u + u2 = 5 Factor a perfect square on the left side: (u + 3)(u + 3) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (u + 3) equal to 2.236067978 and -2.236067978.Subproblem 1
u + 3 = 2.236067978 Simplifying u + 3 = 2.236067978 Reorder the terms: 3 + u = 2.236067978 Solving 3 + u = 2.236067978 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + u = 2.236067978 + -3 Combine like terms: 3 + -3 = 0 0 + u = 2.236067978 + -3 u = 2.236067978 + -3 Combine like terms: 2.236067978 + -3 = -0.763932022 u = -0.763932022 Simplifying u = -0.763932022Subproblem 2
u + 3 = -2.236067978 Simplifying u + 3 = -2.236067978 Reorder the terms: 3 + u = -2.236067978 Solving 3 + u = -2.236067978 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + u = -2.236067978 + -3 Combine like terms: 3 + -3 = 0 0 + u = -2.236067978 + -3 u = -2.236067978 + -3 Combine like terms: -2.236067978 + -3 = -5.236067978 u = -5.236067978 Simplifying u = -5.236067978Solution
The solution to the problem is based on the solutions from the subproblems. u = {-0.763932022, -5.236067978}Solution
u = {-0.763932022, -5.236067978}
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