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Simplifying (-2u2 + -7u + -6) + -1(4u2 + -5u + 8) + (2u2 + -7u + 7) = 0 Reorder the terms: (-6 + -7u + -2u2) + -1(4u2 + -5u + 8) + (2u2 + -7u + 7) = 0 Remove parenthesis around (-6 + -7u + -2u2) -6 + -7u + -2u2 + -1(4u2 + -5u + 8) + (2u2 + -7u + 7) = 0 Reorder the terms: -6 + -7u + -2u2 + -1(8 + -5u + 4u2) + (2u2 + -7u + 7) = 0 -6 + -7u + -2u2 + (8 * -1 + -5u * -1 + 4u2 * -1) + (2u2 + -7u + 7) = 0 -6 + -7u + -2u2 + (-8 + 5u + -4u2) + (2u2 + -7u + 7) = 0 Reorder the terms: -6 + -7u + -2u2 + -8 + 5u + -4u2 + (7 + -7u + 2u2) = 0 Remove parenthesis around (7 + -7u + 2u2) -6 + -7u + -2u2 + -8 + 5u + -4u2 + 7 + -7u + 2u2 = 0 Reorder the terms: -6 + -8 + 7 + -7u + 5u + -7u + -2u2 + -4u2 + 2u2 = 0 Combine like terms: -6 + -8 = -14 -14 + 7 + -7u + 5u + -7u + -2u2 + -4u2 + 2u2 = 0 Combine like terms: -14 + 7 = -7 -7 + -7u + 5u + -7u + -2u2 + -4u2 + 2u2 = 0 Combine like terms: -7u + 5u = -2u -7 + -2u + -7u + -2u2 + -4u2 + 2u2 = 0 Combine like terms: -2u + -7u = -9u -7 + -9u + -2u2 + -4u2 + 2u2 = 0 Combine like terms: -2u2 + -4u2 = -6u2 -7 + -9u + -6u2 + 2u2 = 0 Combine like terms: -6u2 + 2u2 = -4u2 -7 + -9u + -4u2 = 0 Solving -7 + -9u + -4u2 = 0 Solving for variable 'u'. Factor out the Greatest Common Factor (GCF), '-1'. -1(7 + 9u + 4u2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(7 + 9u + 4u2)' equal to zero and attempt to solve: Simplifying 7 + 9u + 4u2 = 0 Solving 7 + 9u + 4u2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.75 + 2.25u + u2 = 0 Move the constant term to the right: Add '-1.75' to each side of the equation. 1.75 + 2.25u + -1.75 + u2 = 0 + -1.75 Reorder the terms: 1.75 + -1.75 + 2.25u + u2 = 0 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + 2.25u + u2 = 0 + -1.75 2.25u + u2 = 0 + -1.75 Combine like terms: 0 + -1.75 = -1.75 2.25u + u2 = -1.75 The u term is 2.25u. Take half its coefficient (1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. 2.25u + 1.265625 + u2 = -1.75 + 1.265625 Reorder the terms: 1.265625 + 2.25u + u2 = -1.75 + 1.265625 Combine like terms: -1.75 + 1.265625 = -0.484375 1.265625 + 2.25u + u2 = -0.484375 Factor a perfect square on the left side: (u + 1.125)(u + 1.125) = -0.484375 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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