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Simplifying (u + -3) = 2u2 + 3u + 29 Reorder the terms: (-3 + u) = 2u2 + 3u + 29 Remove parenthesis around (-3 + u) -3 + u = 2u2 + 3u + 29 Reorder the terms: -3 + u = 29 + 3u + 2u2 Solving -3 + u = 29 + 3u + 2u2 Solving for variable 'u'. Reorder the terms: -3 + -29 + u + -3u + -2u2 = 29 + 3u + 2u2 + -29 + -3u + -2u2 Combine like terms: -3 + -29 = -32 -32 + u + -3u + -2u2 = 29 + 3u + 2u2 + -29 + -3u + -2u2 Combine like terms: u + -3u = -2u -32 + -2u + -2u2 = 29 + 3u + 2u2 + -29 + -3u + -2u2 Reorder the terms: -32 + -2u + -2u2 = 29 + -29 + 3u + -3u + 2u2 + -2u2 Combine like terms: 29 + -29 = 0 -32 + -2u + -2u2 = 0 + 3u + -3u + 2u2 + -2u2 -32 + -2u + -2u2 = 3u + -3u + 2u2 + -2u2 Combine like terms: 3u + -3u = 0 -32 + -2u + -2u2 = 0 + 2u2 + -2u2 -32 + -2u + -2u2 = 2u2 + -2u2 Combine like terms: 2u2 + -2u2 = 0 -32 + -2u + -2u2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(16 + u + u2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(16 + u + u2)' equal to zero and attempt to solve: Simplifying 16 + u + u2 = 0 Solving 16 + u + u2 = 0 Begin completing the square. Move the constant term to the right: Add '-16' to each side of the equation. 16 + u + -16 + u2 = 0 + -16 Reorder the terms: 16 + -16 + u + u2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + u + u2 = 0 + -16 u + u2 = 0 + -16 Combine like terms: 0 + -16 = -16 u + u2 = -16 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 = -16 + 0.25 Reorder the terms: 0.25 + u + u2 = -16 + 0.25 Combine like terms: -16 + 0.25 = -15.75 0.25 + u + u2 = -15.75 Factor a perfect square on the left side: (u + 0.5)(u + 0.5) = -15.75 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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