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Simplifying (7u2 + -1u + -2) + (5u2 + -6u + 3) = 0 Reorder the terms: (-2 + -1u + 7u2) + (5u2 + -6u + 3) = 0 Remove parenthesis around (-2 + -1u + 7u2) -2 + -1u + 7u2 + (5u2 + -6u + 3) = 0 Reorder the terms: -2 + -1u + 7u2 + (3 + -6u + 5u2) = 0 Remove parenthesis around (3 + -6u + 5u2) -2 + -1u + 7u2 + 3 + -6u + 5u2 = 0 Reorder the terms: -2 + 3 + -1u + -6u + 7u2 + 5u2 = 0 Combine like terms: -2 + 3 = 1 1 + -1u + -6u + 7u2 + 5u2 = 0 Combine like terms: -1u + -6u = -7u 1 + -7u + 7u2 + 5u2 = 0 Combine like terms: 7u2 + 5u2 = 12u2 1 + -7u + 12u2 = 0 Solving 1 + -7u + 12u2 = 0 Solving for variable 'u'. Factor a trinomial. (1 + -4u)(1 + -3u) = 0Subproblem 1
Set the factor '(1 + -4u)' equal to zero and attempt to solve: Simplifying 1 + -4u = 0 Solving 1 + -4u = 0 Move all terms containing u to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -4u = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4u = 0 + -1 -4u = 0 + -1 Combine like terms: 0 + -1 = -1 -4u = -1 Divide each side by '-4'. u = 0.25 Simplifying u = 0.25Subproblem 2
Set the factor '(1 + -3u)' equal to zero and attempt to solve: Simplifying 1 + -3u = 0 Solving 1 + -3u = 0 Move all terms containing u to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -3u = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3u = 0 + -1 -3u = 0 + -1 Combine like terms: 0 + -1 = -1 -3u = -1 Divide each side by '-3'. u = 0.3333333333 Simplifying u = 0.3333333333Solution
u = {0.25, 0.3333333333}
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