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Simplifying (u2 + -3u + 4) + (-6u2 + 2u + 7) = 0 Reorder the terms: (4 + -3u + u2) + (-6u2 + 2u + 7) = 0 Remove parenthesis around (4 + -3u + u2) 4 + -3u + u2 + (-6u2 + 2u + 7) = 0 Reorder the terms: 4 + -3u + u2 + (7 + 2u + -6u2) = 0 Remove parenthesis around (7 + 2u + -6u2) 4 + -3u + u2 + 7 + 2u + -6u2 = 0 Reorder the terms: 4 + 7 + -3u + 2u + u2 + -6u2 = 0 Combine like terms: 4 + 7 = 11 11 + -3u + 2u + u2 + -6u2 = 0 Combine like terms: -3u + 2u = -1u 11 + -1u + u2 + -6u2 = 0 Combine like terms: u2 + -6u2 = -5u2 11 + -1u + -5u2 = 0 Solving 11 + -1u + -5u2 = 0 Solving for variable 'u'. Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -2.2 + 0.2u + u2 = 0 Move the constant term to the right: Add '2.2' to each side of the equation. -2.2 + 0.2u + 2.2 + u2 = 0 + 2.2 Reorder the terms: -2.2 + 2.2 + 0.2u + u2 = 0 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + 0.2u + u2 = 0 + 2.2 0.2u + u2 = 0 + 2.2 Combine like terms: 0 + 2.2 = 2.2 0.2u + u2 = 2.2 The u term is 0.2u. Take half its coefficient (0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. 0.2u + 0.01 + u2 = 2.2 + 0.01 Reorder the terms: 0.01 + 0.2u + u2 = 2.2 + 0.01 Combine like terms: 2.2 + 0.01 = 2.21 0.01 + 0.2u + u2 = 2.21 Factor a perfect square on the left side: (u + 0.1)(u + 0.1) = 2.21 Calculate the square root of the right side: 1.486606875 Break this problem into two subproblems by setting (u + 0.1) equal to 1.486606875 and -1.486606875.Subproblem 1
u + 0.1 = 1.486606875 Simplifying u + 0.1 = 1.486606875 Reorder the terms: 0.1 + u = 1.486606875 Solving 0.1 + u = 1.486606875 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + u = 1.486606875 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + u = 1.486606875 + -0.1 u = 1.486606875 + -0.1 Combine like terms: 1.486606875 + -0.1 = 1.386606875 u = 1.386606875 Simplifying u = 1.386606875Subproblem 2
u + 0.1 = -1.486606875 Simplifying u + 0.1 = -1.486606875 Reorder the terms: 0.1 + u = -1.486606875 Solving 0.1 + u = -1.486606875 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + u = -1.486606875 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + u = -1.486606875 + -0.1 u = -1.486606875 + -0.1 Combine like terms: -1.486606875 + -0.1 = -1.586606875 u = -1.586606875 Simplifying u = -1.586606875Solution
The solution to the problem is based on the solutions from the subproblems. u = {1.386606875, -1.586606875}
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