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Simplifying (4u2 + -20u + 25) + -1(16u2 + -88u + 121) = 0 Reorder the terms: (25 + -20u + 4u2) + -1(16u2 + -88u + 121) = 0 Remove parenthesis around (25 + -20u + 4u2) 25 + -20u + 4u2 + -1(16u2 + -88u + 121) = 0 Reorder the terms: 25 + -20u + 4u2 + -1(121 + -88u + 16u2) = 0 25 + -20u + 4u2 + (121 * -1 + -88u * -1 + 16u2 * -1) = 0 25 + -20u + 4u2 + (-121 + 88u + -16u2) = 0 Reorder the terms: 25 + -121 + -20u + 88u + 4u2 + -16u2 = 0 Combine like terms: 25 + -121 = -96 -96 + -20u + 88u + 4u2 + -16u2 = 0 Combine like terms: -20u + 88u = 68u -96 + 68u + 4u2 + -16u2 = 0 Combine like terms: 4u2 + -16u2 = -12u2 -96 + 68u + -12u2 = 0 Solving -96 + 68u + -12u2 = 0 Solving for variable 'u'. Factor out the Greatest Common Factor (GCF), '4'. 4(-24 + 17u + -3u2) = 0 Factor a trinomial. 4((-3 + u)(8 + -3u)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-3 + u)' equal to zero and attempt to solve: Simplifying -3 + u = 0 Solving -3 + u = 0 Move all terms containing u to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + u = 0 + 3 Combine like terms: -3 + 3 = 0 0 + u = 0 + 3 u = 0 + 3 Combine like terms: 0 + 3 = 3 u = 3 Simplifying u = 3Subproblem 2
Set the factor '(8 + -3u)' equal to zero and attempt to solve: Simplifying 8 + -3u = 0 Solving 8 + -3u = 0 Move all terms containing u to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -3u = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -3u = 0 + -8 -3u = 0 + -8 Combine like terms: 0 + -8 = -8 -3u = -8 Divide each side by '-3'. u = 2.666666667 Simplifying u = 2.666666667Solution
u = {3, 2.666666667}
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