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Simplifying (5u2 + 5u + -7) + -1(-2u2 + 9u + 7) + (5u2 + -3u + -5) = 0 Reorder the terms: (-7 + 5u + 5u2) + -1(-2u2 + 9u + 7) + (5u2 + -3u + -5) = 0 Remove parenthesis around (-7 + 5u + 5u2) -7 + 5u + 5u2 + -1(-2u2 + 9u + 7) + (5u2 + -3u + -5) = 0 Reorder the terms: -7 + 5u + 5u2 + -1(7 + 9u + -2u2) + (5u2 + -3u + -5) = 0 -7 + 5u + 5u2 + (7 * -1 + 9u * -1 + -2u2 * -1) + (5u2 + -3u + -5) = 0 -7 + 5u + 5u2 + (-7 + -9u + 2u2) + (5u2 + -3u + -5) = 0 Reorder the terms: -7 + 5u + 5u2 + -7 + -9u + 2u2 + (-5 + -3u + 5u2) = 0 Remove parenthesis around (-5 + -3u + 5u2) -7 + 5u + 5u2 + -7 + -9u + 2u2 + -5 + -3u + 5u2 = 0 Reorder the terms: -7 + -7 + -5 + 5u + -9u + -3u + 5u2 + 2u2 + 5u2 = 0 Combine like terms: -7 + -7 = -14 -14 + -5 + 5u + -9u + -3u + 5u2 + 2u2 + 5u2 = 0 Combine like terms: -14 + -5 = -19 -19 + 5u + -9u + -3u + 5u2 + 2u2 + 5u2 = 0 Combine like terms: 5u + -9u = -4u -19 + -4u + -3u + 5u2 + 2u2 + 5u2 = 0 Combine like terms: -4u + -3u = -7u -19 + -7u + 5u2 + 2u2 + 5u2 = 0 Combine like terms: 5u2 + 2u2 = 7u2 -19 + -7u + 7u2 + 5u2 = 0 Combine like terms: 7u2 + 5u2 = 12u2 -19 + -7u + 12u2 = 0 Solving -19 + -7u + 12u2 = 0 Solving for variable 'u'. Factor a trinomial. (-1 + -1u)(19 + -12u) = 0Subproblem 1
Set the factor '(-1 + -1u)' equal to zero and attempt to solve: Simplifying -1 + -1u = 0 Solving -1 + -1u = 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 + -1u = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1u = 0 + 1 -1u = 0 + 1 Combine like terms: 0 + 1 = 1 -1u = 1 Divide each side by '-1'. u = -1 Simplifying u = -1Subproblem 2
Set the factor '(19 + -12u)' equal to zero and attempt to solve: Simplifying 19 + -12u = 0 Solving 19 + -12u = 0 Move all terms containing u to the left, all other terms to the right. Add '-19' to each side of the equation. 19 + -19 + -12u = 0 + -19 Combine like terms: 19 + -19 = 0 0 + -12u = 0 + -19 -12u = 0 + -19 Combine like terms: 0 + -19 = -19 -12u = -19 Divide each side by '-12'. u = 1.583333333 Simplifying u = 1.583333333Solution
u = {-1, 1.583333333}
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