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Simplifying -2u(4u + -8) + u = 3(u + 6) Reorder the terms: -2u(-8 + 4u) + u = 3(u + 6) (-8 * -2u + 4u * -2u) + u = 3(u + 6) (16u + -8u2) + u = 3(u + 6) Reorder the terms: 16u + u + -8u2 = 3(u + 6) Combine like terms: 16u + u = 17u 17u + -8u2 = 3(u + 6) Reorder the terms: 17u + -8u2 = 3(6 + u) 17u + -8u2 = (6 * 3 + u * 3) 17u + -8u2 = (18 + 3u) Solving 17u + -8u2 = 18 + 3u Solving for variable 'u'. Reorder the terms: -18 + 17u + -3u + -8u2 = 18 + 3u + -18 + -3u Combine like terms: 17u + -3u = 14u -18 + 14u + -8u2 = 18 + 3u + -18 + -3u Reorder the terms: -18 + 14u + -8u2 = 18 + -18 + 3u + -3u Combine like terms: 18 + -18 = 0 -18 + 14u + -8u2 = 0 + 3u + -3u -18 + 14u + -8u2 = 3u + -3u Combine like terms: 3u + -3u = 0 -18 + 14u + -8u2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-9 + 7u + -4u2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-9 + 7u + -4u2)' equal to zero and attempt to solve: Simplifying -9 + 7u + -4u2 = 0 Solving -9 + 7u + -4u2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 2.25 + -1.75u + u2 = 0 Move the constant term to the right: Add '-2.25' to each side of the equation. 2.25 + -1.75u + -2.25 + u2 = 0 + -2.25 Reorder the terms: 2.25 + -2.25 + -1.75u + u2 = 0 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + -1.75u + u2 = 0 + -2.25 -1.75u + u2 = 0 + -2.25 Combine like terms: 0 + -2.25 = -2.25 -1.75u + u2 = -2.25 The u term is -1.75u. Take half its coefficient (-0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. -1.75u + 0.765625 + u2 = -2.25 + 0.765625 Reorder the terms: 0.765625 + -1.75u + u2 = -2.25 + 0.765625 Combine like terms: -2.25 + 0.765625 = -1.484375 0.765625 + -1.75u + u2 = -1.484375 Factor a perfect square on the left side: (u + -0.875)(u + -0.875) = -1.484375 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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