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Simplifying 4x2 + -2(k + -2) * x + -2k = 0 Reorder the terms: 4x2 + -2(-2 + k) * x + -2k = 0 Reorder the terms for easier multiplication: 4x2 + -2x(-2 + k) + -2k = 0 4x2 + (-2 * -2x + k * -2x) + -2k = 0 Reorder the terms: 4x2 + (-2kx + 4x) + -2k = 0 4x2 + (-2kx + 4x) + -2k = 0 Reorder the terms: -2k + -2kx + 4x + 4x2 = 0 Solving -2k + -2kx + 4x + 4x2 = 0 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-4x' to each side of the equation. -2k + -2kx + 4x + -4x + 4x2 = 0 + -4x Combine like terms: 4x + -4x = 0 -2k + -2kx + 0 + 4x2 = 0 + -4x -2k + -2kx + 4x2 = 0 + -4x Remove the zero: -2k + -2kx + 4x2 = -4x Add '-4x2' to each side of the equation. -2k + -2kx + 4x2 + -4x2 = -4x + -4x2 Combine like terms: 4x2 + -4x2 = 0 -2k + -2kx + 0 = -4x + -4x2 -2k + -2kx = -4x + -4x2 Reorder the terms: -2k + -2kx + 4x + 4x2 = -4x + 4x + -4x2 + 4x2 Combine like terms: -4x + 4x = 0 -2k + -2kx + 4x + 4x2 = 0 + -4x2 + 4x2 -2k + -2kx + 4x + 4x2 = -4x2 + 4x2 Combine like terms: -4x2 + 4x2 = 0 -2k + -2kx + 4x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1k + -1kx + 2x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1k + -1kx + 2x + 2x2)' equal to zero and attempt to solve: Simplifying -1k + -1kx + 2x + 2x2 = 0 Solving -1k + -1kx + 2x + 2x2 = 0 Move all terms containing k to the left, all other terms to the right. Add '-2x' to each side of the equation. -1k + -1kx + 2x + -2x + 2x2 = 0 + -2x Combine like terms: 2x + -2x = 0 -1k + -1kx + 0 + 2x2 = 0 + -2x -1k + -1kx + 2x2 = 0 + -2x Remove the zero: -1k + -1kx + 2x2 = -2x Add '-2x2' to each side of the equation. -1k + -1kx + 2x2 + -2x2 = -2x + -2x2 Combine like terms: 2x2 + -2x2 = 0 -1k + -1kx + 0 = -2x + -2x2 -1k + -1kx = -2x + -2x2 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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