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Simplifying 4u2 + 14u + 30 = 0 Reorder the terms: 30 + 14u + 4u2 = 0 Solving 30 + 14u + 4u2 = 0 Solving for variable 'u'. Factor out the Greatest Common Factor (GCF), '2'. 2(15 + 7u + 2u2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(15 + 7u + 2u2)' equal to zero and attempt to solve: Simplifying 15 + 7u + 2u2 = 0 Solving 15 + 7u + 2u2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 7.5 + 3.5u + u2 = 0 Move the constant term to the right: Add '-7.5' to each side of the equation. 7.5 + 3.5u + -7.5 + u2 = 0 + -7.5 Reorder the terms: 7.5 + -7.5 + 3.5u + u2 = 0 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + 3.5u + u2 = 0 + -7.5 3.5u + u2 = 0 + -7.5 Combine like terms: 0 + -7.5 = -7.5 3.5u + u2 = -7.5 The u term is 3.5u. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5u + 3.0625 + u2 = -7.5 + 3.0625 Reorder the terms: 3.0625 + 3.5u + u2 = -7.5 + 3.0625 Combine like terms: -7.5 + 3.0625 = -4.4375 3.0625 + 3.5u + u2 = -4.4375 Factor a perfect square on the left side: (u + 1.75)(u + 1.75) = -4.4375 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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