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Simplifying u2 + -5u + -36 = (2u + -9)(u + 3) Reorder the terms: -36 + -5u + u2 = (2u + -9)(u + 3) Reorder the terms: -36 + -5u + u2 = (-9 + 2u)(u + 3) Reorder the terms: -36 + -5u + u2 = (-9 + 2u)(3 + u) Multiply (-9 + 2u) * (3 + u) -36 + -5u + u2 = (-9(3 + u) + 2u * (3 + u)) -36 + -5u + u2 = ((3 * -9 + u * -9) + 2u * (3 + u)) -36 + -5u + u2 = ((-27 + -9u) + 2u * (3 + u)) -36 + -5u + u2 = (-27 + -9u + (3 * 2u + u * 2u)) -36 + -5u + u2 = (-27 + -9u + (6u + 2u2)) Combine like terms: -9u + 6u = -3u -36 + -5u + u2 = (-27 + -3u + 2u2) Solving -36 + -5u + u2 = -27 + -3u + 2u2 Solving for variable 'u'. Reorder the terms: -36 + 27 + -5u + 3u + u2 + -2u2 = -27 + -3u + 2u2 + 27 + 3u + -2u2 Combine like terms: -36 + 27 = -9 -9 + -5u + 3u + u2 + -2u2 = -27 + -3u + 2u2 + 27 + 3u + -2u2 Combine like terms: -5u + 3u = -2u -9 + -2u + u2 + -2u2 = -27 + -3u + 2u2 + 27 + 3u + -2u2 Combine like terms: u2 + -2u2 = -1u2 -9 + -2u + -1u2 = -27 + -3u + 2u2 + 27 + 3u + -2u2 Reorder the terms: -9 + -2u + -1u2 = -27 + 27 + -3u + 3u + 2u2 + -2u2 Combine like terms: -27 + 27 = 0 -9 + -2u + -1u2 = 0 + -3u + 3u + 2u2 + -2u2 -9 + -2u + -1u2 = -3u + 3u + 2u2 + -2u2 Combine like terms: -3u + 3u = 0 -9 + -2u + -1u2 = 0 + 2u2 + -2u2 -9 + -2u + -1u2 = 2u2 + -2u2 Combine like terms: 2u2 + -2u2 = 0 -9 + -2u + -1u2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(9 + 2u + u2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(9 + 2u + u2)' equal to zero and attempt to solve: Simplifying 9 + 2u + u2 = 0 Solving 9 + 2u + u2 = 0 Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + 2u + -9 + u2 = 0 + -9 Reorder the terms: 9 + -9 + 2u + u2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 2u + u2 = 0 + -9 2u + u2 = 0 + -9 Combine like terms: 0 + -9 = -9 2u + u2 = -9 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 = -9 + 1 Reorder the terms: 1 + 2u + u2 = -9 + 1 Combine like terms: -9 + 1 = -8 1 + 2u + u2 = -8 Factor a perfect square on the left side: (u + 1)(u + 1) = -8 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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