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Simplifying (2u2 + 4u + -3) + -1(-7u2 + 4u + 9) + (5u2 + 5u + -7) = 0 Reorder the terms: (-3 + 4u + 2u2) + -1(-7u2 + 4u + 9) + (5u2 + 5u + -7) = 0 Remove parenthesis around (-3 + 4u + 2u2) -3 + 4u + 2u2 + -1(-7u2 + 4u + 9) + (5u2 + 5u + -7) = 0 Reorder the terms: -3 + 4u + 2u2 + -1(9 + 4u + -7u2) + (5u2 + 5u + -7) = 0 -3 + 4u + 2u2 + (9 * -1 + 4u * -1 + -7u2 * -1) + (5u2 + 5u + -7) = 0 -3 + 4u + 2u2 + (-9 + -4u + 7u2) + (5u2 + 5u + -7) = 0 Reorder the terms: -3 + 4u + 2u2 + -9 + -4u + 7u2 + (-7 + 5u + 5u2) = 0 Remove parenthesis around (-7 + 5u + 5u2) -3 + 4u + 2u2 + -9 + -4u + 7u2 + -7 + 5u + 5u2 = 0 Reorder the terms: -3 + -9 + -7 + 4u + -4u + 5u + 2u2 + 7u2 + 5u2 = 0 Combine like terms: -3 + -9 = -12 -12 + -7 + 4u + -4u + 5u + 2u2 + 7u2 + 5u2 = 0 Combine like terms: -12 + -7 = -19 -19 + 4u + -4u + 5u + 2u2 + 7u2 + 5u2 = 0 Combine like terms: 4u + -4u = 0 -19 + 0 + 5u + 2u2 + 7u2 + 5u2 = 0 -19 + 5u + 2u2 + 7u2 + 5u2 = 0 Combine like terms: 2u2 + 7u2 = 9u2 -19 + 5u + 9u2 + 5u2 = 0 Combine like terms: 9u2 + 5u2 = 14u2 -19 + 5u + 14u2 = 0 Solving -19 + 5u + 14u2 = 0 Solving for variable 'u'. Factor a trinomial. (-19 + -14u)(1 + -1u) = 0Subproblem 1
Set the factor '(-19 + -14u)' equal to zero and attempt to solve: Simplifying -19 + -14u = 0 Solving -19 + -14u = 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 + -14u = 0 + 19 Combine like terms: -19 + 19 = 0 0 + -14u = 0 + 19 -14u = 0 + 19 Combine like terms: 0 + 19 = 19 -14u = 19 Divide each side by '-14'. u = -1.357142857 Simplifying u = -1.357142857Subproblem 2
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 = 1Solution
u = {-1.357142857, 1}
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