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Simplifying (2u2 + -6u + 7) + (-3u2 + 5u + 1) = 0 Reorder the terms: (7 + -6u + 2u2) + (-3u2 + 5u + 1) = 0 Remove parenthesis around (7 + -6u + 2u2) 7 + -6u + 2u2 + (-3u2 + 5u + 1) = 0 Reorder the terms: 7 + -6u + 2u2 + (1 + 5u + -3u2) = 0 Remove parenthesis around (1 + 5u + -3u2) 7 + -6u + 2u2 + 1 + 5u + -3u2 = 0 Reorder the terms: 7 + 1 + -6u + 5u + 2u2 + -3u2 = 0 Combine like terms: 7 + 1 = 8 8 + -6u + 5u + 2u2 + -3u2 = 0 Combine like terms: -6u + 5u = -1u 8 + -1u + 2u2 + -3u2 = 0 Combine like terms: 2u2 + -3u2 = -1u2 8 + -1u + -1u2 = 0 Solving 8 + -1u + -1u2 = 0 Solving for variable 'u'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -8 + u + u2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + u + 8 + u2 = 0 + 8 Reorder the terms: -8 + 8 + u + u2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + u + u2 = 0 + 8 u + u2 = 0 + 8 Combine like terms: 0 + 8 = 8 u + u2 = 8 The u term is u. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + u2 = 8 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + u2 = 8 + 0.25 Combine like terms: 8 + 0.25 = 8.25 1.25 + u2 = 8.25 Factor a perfect square on the left side: (u + 0.5)(u + 0.5) = 8.25 Calculate the square root of the right side: 2.872281323 Break this problem into two subproblems by setting (u + 0.5) equal to 2.872281323 and -2.872281323.Subproblem 1
u + 0.5 = 2.872281323 Simplifying u + 0.5 = 2.872281323 Reorder the terms: 0.5 + u = 2.872281323 Solving 0.5 + u = 2.872281323 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + u = 2.872281323 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + u = 2.872281323 + -0.5 u = 2.872281323 + -0.5 Combine like terms: 2.872281323 + -0.5 = 2.372281323 u = 2.372281323 Simplifying u = 2.372281323Subproblem 2
u + 0.5 = -2.872281323 Simplifying u + 0.5 = -2.872281323 Reorder the terms: 0.5 + u = -2.872281323 Solving 0.5 + u = -2.872281323 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + u = -2.872281323 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + u = -2.872281323 + -0.5 u = -2.872281323 + -0.5 Combine like terms: -2.872281323 + -0.5 = -3.372281323 u = -3.372281323 Simplifying u = -3.372281323Solution
The solution to the problem is based on the solutions from the subproblems. u = {2.372281323, -3.372281323}
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