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Simplifying 6u2 + 6u = -20 Reorder the terms: 6u + 6u2 = -20 Solving 6u + 6u2 = -20 Solving for variable 'u'. Reorder the terms: 20 + 6u + 6u2 = -20 + 20 Combine like terms: -20 + 20 = 0 20 + 6u + 6u2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(10 + 3u + 3u2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(10 + 3u + 3u2)' equal to zero and attempt to solve: Simplifying 10 + 3u + 3u2 = 0 Solving 10 + 3u + 3u2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 3.333333333 + u + u2 = 0 Move the constant term to the right: Add '-3.333333333' to each side of the equation. 3.333333333 + u + -3.333333333 + u2 = 0 + -3.333333333 Reorder the terms: 3.333333333 + -3.333333333 + u + u2 = 0 + -3.333333333 Combine like terms: 3.333333333 + -3.333333333 = 0.000000000 0.000000000 + u + u2 = 0 + -3.333333333 u + u2 = 0 + -3.333333333 Combine like terms: 0 + -3.333333333 = -3.333333333 u + u2 = -3.333333333 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. + 0.25 + u2 = -3.333333333 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + u2 = -3.333333333 + 0.25 Combine like terms: -3.333333333 + 0.25 = -3.083333333 1.25 + u2 = -3.083333333 Factor a perfect square on the left side: (u + 0.5)(u + 0.5) = -3.083333333 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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