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Simplifying 8u(4u + -1) + -12u = 11(2u + -6) Reorder the terms: 8u(-1 + 4u) + -12u = 11(2u + -6) (-1 * 8u + 4u * 8u) + -12u = 11(2u + -6) (-8u + 32u2) + -12u = 11(2u + -6) Reorder the terms: -8u + -12u + 32u2 = 11(2u + -6) Combine like terms: -8u + -12u = -20u -20u + 32u2 = 11(2u + -6) Reorder the terms: -20u + 32u2 = 11(-6 + 2u) -20u + 32u2 = (-6 * 11 + 2u * 11) -20u + 32u2 = (-66 + 22u) Solving -20u + 32u2 = -66 + 22u Solving for variable 'u'. Reorder the terms: 66 + -20u + -22u + 32u2 = -66 + 22u + 66 + -22u Combine like terms: -20u + -22u = -42u 66 + -42u + 32u2 = -66 + 22u + 66 + -22u Reorder the terms: 66 + -42u + 32u2 = -66 + 66 + 22u + -22u Combine like terms: -66 + 66 = 0 66 + -42u + 32u2 = 0 + 22u + -22u 66 + -42u + 32u2 = 22u + -22u Combine like terms: 22u + -22u = 0 66 + -42u + 32u2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(33 + -21u + 16u2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(33 + -21u + 16u2)' equal to zero and attempt to solve: Simplifying 33 + -21u + 16u2 = 0 Solving 33 + -21u + 16u2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 2.0625 + -1.3125u + u2 = 0 Move the constant term to the right: Add '-2.0625' to each side of the equation. 2.0625 + -1.3125u + -2.0625 + u2 = 0 + -2.0625 Reorder the terms: 2.0625 + -2.0625 + -1.3125u + u2 = 0 + -2.0625 Combine like terms: 2.0625 + -2.0625 = 0.0000 0.0000 + -1.3125u + u2 = 0 + -2.0625 -1.3125u + u2 = 0 + -2.0625 Combine like terms: 0 + -2.0625 = -2.0625 -1.3125u + u2 = -2.0625 The u term is -1.3125u. Take half its coefficient (-0.65625). Square it (0.4306640625) and add it to both sides. Add '0.4306640625' to each side of the equation. -1.3125u + 0.4306640625 + u2 = -2.0625 + 0.4306640625 Reorder the terms: 0.4306640625 + -1.3125u + u2 = -2.0625 + 0.4306640625 Combine like terms: -2.0625 + 0.4306640625 = -1.6318359375 0.4306640625 + -1.3125u + u2 = -1.6318359375 Factor a perfect square on the left side: (u + -0.65625)(u + -0.65625) = -1.6318359375 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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