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Simplifying 8u(4u + -1) + -12 = 11(2u + -6) Reorder the terms: 8u(-1 + 4u) + -12 = 11(2u + -6) (-1 * 8u + 4u * 8u) + -12 = 11(2u + -6) (-8u + 32u2) + -12 = 11(2u + -6) Reorder the terms: -12 + -8u + 32u2 = 11(2u + -6) Reorder the terms: -12 + -8u + 32u2 = 11(-6 + 2u) -12 + -8u + 32u2 = (-6 * 11 + 2u * 11) -12 + -8u + 32u2 = (-66 + 22u) Solving -12 + -8u + 32u2 = -66 + 22u Solving for variable 'u'. Reorder the terms: -12 + 66 + -8u + -22u + 32u2 = -66 + 22u + 66 + -22u Combine like terms: -12 + 66 = 54 54 + -8u + -22u + 32u2 = -66 + 22u + 66 + -22u Combine like terms: -8u + -22u = -30u 54 + -30u + 32u2 = -66 + 22u + 66 + -22u Reorder the terms: 54 + -30u + 32u2 = -66 + 66 + 22u + -22u Combine like terms: -66 + 66 = 0 54 + -30u + 32u2 = 0 + 22u + -22u 54 + -30u + 32u2 = 22u + -22u Combine like terms: 22u + -22u = 0 54 + -30u + 32u2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(27 + -15u + 16u2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(27 + -15u + 16u2)' equal to zero and attempt to solve: Simplifying 27 + -15u + 16u2 = 0 Solving 27 + -15u + 16u2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 1.6875 + -0.9375u + u2 = 0 Move the constant term to the right: Add '-1.6875' to each side of the equation. 1.6875 + -0.9375u + -1.6875 + u2 = 0 + -1.6875 Reorder the terms: 1.6875 + -1.6875 + -0.9375u + u2 = 0 + -1.6875 Combine like terms: 1.6875 + -1.6875 = 0.0000 0.0000 + -0.9375u + u2 = 0 + -1.6875 -0.9375u + u2 = 0 + -1.6875 Combine like terms: 0 + -1.6875 = -1.6875 -0.9375u + u2 = -1.6875 The u term is -0.9375u. Take half its coefficient (-0.46875). Square it (0.2197265625) and add it to both sides. Add '0.2197265625' to each side of the equation. -0.9375u + 0.2197265625 + u2 = -1.6875 + 0.2197265625 Reorder the terms: 0.2197265625 + -0.9375u + u2 = -1.6875 + 0.2197265625 Combine like terms: -1.6875 + 0.2197265625 = -1.4677734375 0.2197265625 + -0.9375u + u2 = -1.4677734375 Factor a perfect square on the left side: (u + -0.46875)(u + -0.46875) = -1.4677734375 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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