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Simplifying (-6u2 + 7u + -5) + (4u2 + 3u + 2) = 0 Reorder the terms: (-5 + 7u + -6u2) + (4u2 + 3u + 2) = 0 Remove parenthesis around (-5 + 7u + -6u2) -5 + 7u + -6u2 + (4u2 + 3u + 2) = 0 Reorder the terms: -5 + 7u + -6u2 + (2 + 3u + 4u2) = 0 Remove parenthesis around (2 + 3u + 4u2) -5 + 7u + -6u2 + 2 + 3u + 4u2 = 0 Reorder the terms: -5 + 2 + 7u + 3u + -6u2 + 4u2 = 0 Combine like terms: -5 + 2 = -3 -3 + 7u + 3u + -6u2 + 4u2 = 0 Combine like terms: 7u + 3u = 10u -3 + 10u + -6u2 + 4u2 = 0 Combine like terms: -6u2 + 4u2 = -2u2 -3 + 10u + -2u2 = 0 Solving -3 + 10u + -2u2 = 0 Solving for variable 'u'. Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 1.5 + -5u + u2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + -5u + -1.5 + u2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + -5u + u2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + -5u + u2 = 0 + -1.5 -5u + u2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 -5u + u2 = -1.5 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 = -1.5 + 6.25 Reorder the terms: 6.25 + -5u + u2 = -1.5 + 6.25 Combine like terms: -1.5 + 6.25 = 4.75 6.25 + -5u + u2 = 4.75 Factor a perfect square on the left side: (u + -2.5)(u + -2.5) = 4.75 Calculate the square root of the right side: 2.179449472 Break this problem into two subproblems by setting (u + -2.5) equal to 2.179449472 and -2.179449472.Subproblem 1
u + -2.5 = 2.179449472 Simplifying u + -2.5 = 2.179449472 Reorder the terms: -2.5 + u = 2.179449472 Solving -2.5 + u = 2.179449472 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 = 2.179449472 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + u = 2.179449472 + 2.5 u = 2.179449472 + 2.5 Combine like terms: 2.179449472 + 2.5 = 4.679449472 u = 4.679449472 Simplifying u = 4.679449472Subproblem 2
u + -2.5 = -2.179449472 Simplifying u + -2.5 = -2.179449472 Reorder the terms: -2.5 + u = -2.179449472 Solving -2.5 + u = -2.179449472 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 = -2.179449472 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + u = -2.179449472 + 2.5 u = -2.179449472 + 2.5 Combine like terms: -2.179449472 + 2.5 = 0.320550528 u = 0.320550528 Simplifying u = 0.320550528Solution
The solution to the problem is based on the solutions from the subproblems. u = {4.679449472, 0.320550528}
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