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Simplifying (2k + -1) * x2 + (k + -3) * x + 3k + -1 = 0 Reorder the terms: (-1 + 2k) * x2 + (k + -3) * x + 3k + -1 = 0 Reorder the terms for easier multiplication: x2(-1 + 2k) + (k + -3) * x + 3k + -1 = 0 (-1 * x2 + 2k * x2) + (k + -3) * x + 3k + -1 = 0 Reorder the terms: (2kx2 + -1x2) + (k + -3) * x + 3k + -1 = 0 (2kx2 + -1x2) + (k + -3) * x + 3k + -1 = 0 Reorder the terms: 2kx2 + -1x2 + (-3 + k) * x + 3k + -1 = 0 Reorder the terms for easier multiplication: 2kx2 + -1x2 + x(-3 + k) + 3k + -1 = 0 2kx2 + -1x2 + (-3 * x + k * x) + 3k + -1 = 0 Reorder the terms: 2kx2 + -1x2 + (kx + -3x) + 3k + -1 = 0 2kx2 + -1x2 + (kx + -3x) + 3k + -1 = 0 Reorder the terms: -1 + 3k + kx + 2kx2 + -3x + -1x2 = 0 Solving -1 + 3k + kx + 2kx2 + -3x + -1x2 = 0 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 3k + kx + 2kx2 + -3x + 1 + -1x2 = 0 + 1 Reorder the terms: -1 + 1 + 3k + kx + 2kx2 + -3x + -1x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 3k + kx + 2kx2 + -3x + -1x2 = 0 + 1 3k + kx + 2kx2 + -3x + -1x2 = 0 + 1 Combine like terms: 0 + 1 = 1 3k + kx + 2kx2 + -3x + -1x2 = 1 Add '3x' to each side of the equation. 3k + kx + 2kx2 + -3x + 3x + -1x2 = 1 + 3x Combine like terms: -3x + 3x = 0 3k + kx + 2kx2 + 0 + -1x2 = 1 + 3x 3k + kx + 2kx2 + -1x2 = 1 + 3x Add 'x2' to each side of the equation. 3k + kx + 2kx2 + -1x2 + x2 = 1 + 3x + x2 Combine like terms: -1x2 + x2 = 0 3k + kx + 2kx2 + 0 = 1 + 3x + x2 3k + kx + 2kx2 = 1 + 3x + x2 Reorder the terms: -1 + 3k + kx + 2kx2 + -3x + -1x2 = 1 + 3x + x2 + -1 + -3x + -1x2 Reorder the terms: -1 + 3k + kx + 2kx2 + -3x + -1x2 = 1 + -1 + 3x + -3x + x2 + -1x2 Combine like terms: 1 + -1 = 0 -1 + 3k + kx + 2kx2 + -3x + -1x2 = 0 + 3x + -3x + x2 + -1x2 -1 + 3k + kx + 2kx2 + -3x + -1x2 = 3x + -3x + x2 + -1x2 Combine like terms: 3x + -3x = 0 -1 + 3k + kx + 2kx2 + -3x + -1x2 = 0 + x2 + -1x2 -1 + 3k + kx + 2kx2 + -3x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -1 + 3k + kx + 2kx2 + -3x + -1x2 = 0 The solution to this equation could not be determined.
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