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Simplifying 2u2 + -18u2 + -4u + -21 = 114 Reorder the terms: -21 + -4u + 2u2 + -18u2 = 114 Combine like terms: 2u2 + -18u2 = -16u2 -21 + -4u + -16u2 = 114 Solving -21 + -4u + -16u2 = 114 Solving for variable 'u'. Reorder the terms: -21 + -114 + -4u + -16u2 = 114 + -114 Combine like terms: -21 + -114 = -135 -135 + -4u + -16u2 = 114 + -114 Combine like terms: 114 + -114 = 0 -135 + -4u + -16u2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(135 + 4u + 16u2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(135 + 4u + 16u2)' equal to zero and attempt to solve: Simplifying 135 + 4u + 16u2 = 0 Solving 135 + 4u + 16u2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 8.4375 + 0.25u + u2 = 0 Move the constant term to the right: Add '-8.4375' to each side of the equation. 8.4375 + 0.25u + -8.4375 + u2 = 0 + -8.4375 Reorder the terms: 8.4375 + -8.4375 + 0.25u + u2 = 0 + -8.4375 Combine like terms: 8.4375 + -8.4375 = 0.0000 0.0000 + 0.25u + u2 = 0 + -8.4375 0.25u + u2 = 0 + -8.4375 Combine like terms: 0 + -8.4375 = -8.4375 0.25u + u2 = -8.4375 The u term is 0.25u. Take half its coefficient (0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. 0.25u + 0.015625 + u2 = -8.4375 + 0.015625 Reorder the terms: 0.015625 + 0.25u + u2 = -8.4375 + 0.015625 Combine like terms: -8.4375 + 0.015625 = -8.421875 0.015625 + 0.25u + u2 = -8.421875 Factor a perfect square on the left side: (u + 0.125)(u + 0.125) = -8.421875 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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