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Simplifying 0 = (K2 + 2k + 2)(3k + 2) Reorder the terms: 0 = (2 + K2 + 2k)(3k + 2) Reorder the terms: 0 = (2 + K2 + 2k)(2 + 3k) Multiply (2 + K2 + 2k) * (2 + 3k) 0 = (2(2 + 3k) + K2(2 + 3k) + 2k * (2 + 3k)) 0 = ((2 * 2 + 3k * 2) + K2(2 + 3k) + 2k * (2 + 3k)) 0 = ((4 + 6k) + K2(2 + 3k) + 2k * (2 + 3k)) 0 = (4 + 6k + (2 * K2 + 3k * K2) + 2k * (2 + 3k)) 0 = (4 + 6k + (2K2 + 3kK2) + 2k * (2 + 3k)) 0 = (4 + 6k + 2K2 + 3kK2 + (2 * 2k + 3k * 2k)) 0 = (4 + 6k + 2K2 + 3kK2 + (4k + 6k2)) Reorder the terms: 0 = (4 + 2K2 + 6k + 4k + 3kK2 + 6k2) Combine like terms: 6k + 4k = 10k 0 = (4 + 2K2 + 10k + 3kK2 + 6k2) Solving 0 = 4 + 2K2 + 10k + 3kK2 + 6k2 Solving for variable 'K'. Move all terms containing K to the left, all other terms to the right. Add '-2K2' to each side of the equation. 0 + -2K2 = 4 + 2K2 + 10k + 3kK2 + -2K2 + 6k2 Remove the zero: -2K2 = 4 + 2K2 + 10k + 3kK2 + -2K2 + 6k2 Reorder the terms: -2K2 = 4 + 2K2 + -2K2 + 10k + 3kK2 + 6k2 Combine like terms: 2K2 + -2K2 = 0 -2K2 = 4 + 0 + 10k + 3kK2 + 6k2 -2K2 = 4 + 10k + 3kK2 + 6k2 Add '-3kK2' to each side of the equation. -2K2 + -3kK2 = 4 + 10k + 3kK2 + -3kK2 + 6k2 Combine like terms: 3kK2 + -3kK2 = 0 -2K2 + -3kK2 = 4 + 10k + 0 + 6k2 -2K2 + -3kK2 = 4 + 10k + 6k2 Reorder the terms: -4 + -2K2 + -10k + -3kK2 + -6k2 = 4 + 10k + 6k2 + -4 + -10k + -6k2 Reorder the terms: -4 + -2K2 + -10k + -3kK2 + -6k2 = 4 + -4 + 10k + -10k + 6k2 + -6k2 Combine like terms: 4 + -4 = 0 -4 + -2K2 + -10k + -3kK2 + -6k2 = 0 + 10k + -10k + 6k2 + -6k2 -4 + -2K2 + -10k + -3kK2 + -6k2 = 10k + -10k + 6k2 + -6k2 Combine like terms: 10k + -10k = 0 -4 + -2K2 + -10k + -3kK2 + -6k2 = 0 + 6k2 + -6k2 -4 + -2K2 + -10k + -3kK2 + -6k2 = 6k2 + -6k2 Combine like terms: 6k2 + -6k2 = 0 -4 + -2K2 + -10k + -3kK2 + -6k2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(4 + 2K2 + 10k + 3kK2 + 6k2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(4 + 2K2 + 10k + 3kK2 + 6k2)' equal to zero and attempt to solve: Simplifying 4 + 2K2 + 10k + 3kK2 + 6k2 = 0 Solving 4 + 2K2 + 10k + 3kK2 + 6k2 = 0 Move all terms containing K to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + 2K2 + 10k + 3kK2 + -4 + 6k2 = 0 + -4 Reorder the terms: 4 + -4 + 2K2 + 10k + 3kK2 + 6k2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 2K2 + 10k + 3kK2 + 6k2 = 0 + -4 2K2 + 10k + 3kK2 + 6k2 = 0 + -4 Combine like terms: 0 + -4 = -4 2K2 + 10k + 3kK2 + 6k2 = -4 Add '-10k' to each side of the equation. 2K2 + 10k + 3kK2 + -10k + 6k2 = -4 + -10k Reorder the terms: 2K2 + 10k + -10k + 3kK2 + 6k2 = -4 + -10k Combine like terms: 10k + -10k = 0 2K2 + 0 + 3kK2 + 6k2 = -4 + -10k 2K2 + 3kK2 + 6k2 = -4 + -10k Add '-6k2' to each side of the equation. 2K2 + 3kK2 + 6k2 + -6k2 = -4 + -10k + -6k2 Combine like terms: 6k2 + -6k2 = 0 2K2 + 3kK2 + 0 = -4 + -10k + -6k2 2K2 + 3kK2 = -4 + -10k + -6k2 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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