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Simplifying 0 = (k + 1) * x2 + x + k Reorder the terms: 0 = (1 + k) * x2 + x + k Reorder the terms for easier multiplication: 0 = x2(1 + k) + x + k 0 = (1 * x2 + k * x2) + x + k Reorder the terms: 0 = (kx2 + 1x2) + x + k 0 = (kx2 + 1x2) + x + k Reorder the terms: 0 = k + kx2 + x + 1x2 Solving 0 = k + kx2 + x + 1x2 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-1k' to each side of the equation. 0 + -1k = k + kx2 + x + -1k + 1x2 Remove the zero: -1k = k + kx2 + x + -1k + 1x2 Reorder the terms: -1k = k + -1k + kx2 + x + 1x2 Combine like terms: k + -1k = 0 -1k = 0 + kx2 + x + 1x2 -1k = kx2 + x + 1x2 Add '-1kx2' to each side of the equation. -1k + -1kx2 = kx2 + x + -1kx2 + 1x2 Reorder the terms: -1k + -1kx2 = kx2 + -1kx2 + x + 1x2 Combine like terms: kx2 + -1kx2 = 0 -1k + -1kx2 = 0 + x + 1x2 -1k + -1kx2 = x + 1x2 Reorder the terms: -1k + -1kx2 + -1x + -1x2 = x + -1x + 1x2 + -1x2 Combine like terms: x + -1x = 0 -1k + -1kx2 + -1x + -1x2 = 0 + 1x2 + -1x2 -1k + -1kx2 + -1x + -1x2 = 1x2 + -1x2 Combine like terms: 1x2 + -1x2 = 0 -1k + -1kx2 + -1x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(k + kx2 + x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(k + kx2 + x + x2)' equal to zero and attempt to solve: Simplifying k + kx2 + x + x2 = 0 Solving k + kx2 + x + x2 = 0 Move all terms containing k to the left, all other terms to the right. Add '-1x' to each side of the equation. k + kx2 + x + -1x + x2 = 0 + -1x Combine like terms: x + -1x = 0 k + kx2 + 0 + x2 = 0 + -1x k + kx2 + x2 = 0 + -1x Remove the zero: k + kx2 + x2 = -1x Add '-1x2' to each side of the equation. k + kx2 + x2 + -1x2 = -1x + -1x2 Combine like terms: x2 + -1x2 = 0 k + kx2 + 0 = -1x + -1x2 k + kx2 = -1x + -1x2 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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