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Simplifying 4(u + 1) * u = 8(u + -1) + 6 Reorder the terms: 4(1 + u) * u = 8(u + -1) + 6 Reorder the terms for easier multiplication: 4u(1 + u) = 8(u + -1) + 6 (1 * 4u + u * 4u) = 8(u + -1) + 6 (4u + 4u2) = 8(u + -1) + 6 Reorder the terms: 4u + 4u2 = 8(-1 + u) + 6 4u + 4u2 = (-1 * 8 + u * 8) + 6 4u + 4u2 = (-8 + 8u) + 6 Reorder the terms: 4u + 4u2 = -8 + 6 + 8u Combine like terms: -8 + 6 = -2 4u + 4u2 = -2 + 8u Solving 4u + 4u2 = -2 + 8u Solving for variable 'u'. Reorder the terms: 2 + 4u + -8u + 4u2 = -2 + 8u + 2 + -8u Combine like terms: 4u + -8u = -4u 2 + -4u + 4u2 = -2 + 8u + 2 + -8u Reorder the terms: 2 + -4u + 4u2 = -2 + 2 + 8u + -8u Combine like terms: -2 + 2 = 0 2 + -4u + 4u2 = 0 + 8u + -8u 2 + -4u + 4u2 = 8u + -8u Combine like terms: 8u + -8u = 0 2 + -4u + 4u2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(1 + -2u + 2u2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + -2u + 2u2)' equal to zero and attempt to solve: Simplifying 1 + -2u + 2u2 = 0 Solving 1 + -2u + 2u2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 0.5 + -1u + u2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -1u + -0.5 + u2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + -1u + u2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -1u + u2 = 0 + -0.5 -1u + u2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 -1u + u2 = -0.5 The u term is -1u. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1u + 0.25 + u2 = -0.5 + 0.25 Reorder the terms: 0.25 + -1u + u2 = -0.5 + 0.25 Combine like terms: -0.5 + 0.25 = -0.25 0.25 + -1u + u2 = -0.25 Factor a perfect square on the left side: (u + -0.5)(u + -0.5) = -0.25 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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