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Simplifying 2u2 + 2(8 + u) = 0 2u2 + (8 * 2 + u * 2) = 0 2u2 + (16 + 2u) = 0 Reorder the terms: 16 + 2u + 2u2 = 0 Solving 16 + 2u + 2u2 = 0 Solving for variable 'u'. Factor out the Greatest Common Factor (GCF), '2'. 2(8 + u + u2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(8 + u + u2)' equal to zero and attempt to solve: Simplifying 8 + u + u2 = 0 Solving 8 + u + u2 = 0 Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + u + -8 + u2 = 0 + -8 Reorder the terms: 8 + -8 + u + u2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + u + u2 = 0 + -8 u + u2 = 0 + -8 Combine like terms: 0 + -8 = -8 u + u2 = -8 The u term is u. 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. u + 0.25 + u2 = -8 + 0.25 Reorder the terms: 0.25 + u + u2 = -8 + 0.25 Combine like terms: -8 + 0.25 = -7.75 0.25 + u + u2 = -7.75 Factor a perfect square on the left side: (u + 0.5)(u + 0.5) = -7.75 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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