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Simplifying 7(8u + -11) = (8u + -11)(8u + -11) Reorder the terms: 7(-11 + 8u) = (8u + -11)(8u + -11) (-11 * 7 + 8u * 7) = (8u + -11)(8u + -11) (-77 + 56u) = (8u + -11)(8u + -11) Reorder the terms: -77 + 56u = (-11 + 8u)(8u + -11) Reorder the terms: -77 + 56u = (-11 + 8u)(-11 + 8u) Multiply (-11 + 8u) * (-11 + 8u) -77 + 56u = (-11(-11 + 8u) + 8u * (-11 + 8u)) -77 + 56u = ((-11 * -11 + 8u * -11) + 8u * (-11 + 8u)) -77 + 56u = ((121 + -88u) + 8u * (-11 + 8u)) -77 + 56u = (121 + -88u + (-11 * 8u + 8u * 8u)) -77 + 56u = (121 + -88u + (-88u + 64u2)) Combine like terms: -88u + -88u = -176u -77 + 56u = (121 + -176u + 64u2) Solving -77 + 56u = 121 + -176u + 64u2 Solving for variable 'u'. Reorder the terms: -77 + -121 + 56u + 176u + -64u2 = 121 + -176u + 64u2 + -121 + 176u + -64u2 Combine like terms: -77 + -121 = -198 -198 + 56u + 176u + -64u2 = 121 + -176u + 64u2 + -121 + 176u + -64u2 Combine like terms: 56u + 176u = 232u -198 + 232u + -64u2 = 121 + -176u + 64u2 + -121 + 176u + -64u2 Reorder the terms: -198 + 232u + -64u2 = 121 + -121 + -176u + 176u + 64u2 + -64u2 Combine like terms: 121 + -121 = 0 -198 + 232u + -64u2 = 0 + -176u + 176u + 64u2 + -64u2 -198 + 232u + -64u2 = -176u + 176u + 64u2 + -64u2 Combine like terms: -176u + 176u = 0 -198 + 232u + -64u2 = 0 + 64u2 + -64u2 -198 + 232u + -64u2 = 64u2 + -64u2 Combine like terms: 64u2 + -64u2 = 0 -198 + 232u + -64u2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-99 + 116u + -32u2) = 0 Factor a trinomial. 2((-9 + 4u)(11 + -8u)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-9 + 4u)' equal to zero and attempt to solve: Simplifying -9 + 4u = 0 Solving -9 + 4u = 0 Move all terms containing u to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + 4u = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 4u = 0 + 9 4u = 0 + 9 Combine like terms: 0 + 9 = 9 4u = 9 Divide each side by '4'. u = 2.25 Simplifying u = 2.25Subproblem 2
Set the factor '(11 + -8u)' equal to zero and attempt to solve: Simplifying 11 + -8u = 0 Solving 11 + -8u = 0 Move all terms containing u to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -8u = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -8u = 0 + -11 -8u = 0 + -11 Combine like terms: 0 + -11 = -11 -8u = -11 Divide each side by '-8'. u = 1.375 Simplifying u = 1.375Solution
u = {2.25, 1.375}
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