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Simplifying (2u2 + -3u + -1) + (5u + -6u + 7) = 0 Reorder the terms: (-1 + -3u + 2u2) + (5u + -6u + 7) = 0 Remove parenthesis around (-1 + -3u + 2u2) -1 + -3u + 2u2 + (5u + -6u + 7) = 0 Reorder the terms: -1 + -3u + 2u2 + (7 + 5u + -6u) = 0 Combine like terms: 5u + -6u = -1u -1 + -3u + 2u2 + (7 + -1u) = 0 Remove parenthesis around (7 + -1u) -1 + -3u + 2u2 + 7 + -1u = 0 Reorder the terms: -1 + 7 + -3u + -1u + 2u2 = 0 Combine like terms: -1 + 7 = 6 6 + -3u + -1u + 2u2 = 0 Combine like terms: -3u + -1u = -4u 6 + -4u + 2u2 = 0 Solving 6 + -4u + 2u2 = 0 Solving for variable 'u'. Factor out the Greatest Common Factor (GCF), '2'. 2(3 + -2u + u2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + -2u + u2)' equal to zero and attempt to solve: Simplifying 3 + -2u + u2 = 0 Solving 3 + -2u + u2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + -2u + -3 + u2 = 0 + -3 Reorder the terms: 3 + -3 + -2u + u2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2u + u2 = 0 + -3 -2u + u2 = 0 + -3 Combine like terms: 0 + -3 = -3 -2u + u2 = -3 The u term is -2u. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2u + 1 + u2 = -3 + 1 Reorder the terms: 1 + -2u + u2 = -3 + 1 Combine like terms: -3 + 1 = -2 1 + -2u + u2 = -2 Factor a perfect square on the left side: (u + -1)(u + -1) = -2 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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