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Simplifying (2k + -1) * x2 + (4k + 1) * x + k + 3 = 0 Reorder the terms: (-1 + 2k) * x2 + (4k + 1) * x + k + 3 = 0 Reorder the terms for easier multiplication: x2(-1 + 2k) + (4k + 1) * x + k + 3 = 0 (-1 * x2 + 2k * x2) + (4k + 1) * x + k + 3 = 0 Reorder the terms: (2kx2 + -1x2) + (4k + 1) * x + k + 3 = 0 (2kx2 + -1x2) + (4k + 1) * x + k + 3 = 0 Reorder the terms: 2kx2 + -1x2 + (1 + 4k) * x + k + 3 = 0 Reorder the terms for easier multiplication: 2kx2 + -1x2 + x(1 + 4k) + k + 3 = 0 2kx2 + -1x2 + (1 * x + 4k * x) + k + 3 = 0 Reorder the terms: 2kx2 + -1x2 + (4kx + 1x) + k + 3 = 0 2kx2 + -1x2 + (4kx + 1x) + k + 3 = 0 Reorder the terms: 3 + k + 4kx + 2kx2 + 1x + -1x2 = 0 Solving 3 + k + 4kx + 2kx2 + 1x + -1x2 = 0 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + k + 4kx + 2kx2 + 1x + -3 + -1x2 = 0 + -3 Reorder the terms: 3 + -3 + k + 4kx + 2kx2 + 1x + -1x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + k + 4kx + 2kx2 + 1x + -1x2 = 0 + -3 k + 4kx + 2kx2 + 1x + -1x2 = 0 + -3 Combine like terms: 0 + -3 = -3 k + 4kx + 2kx2 + 1x + -1x2 = -3 Add '-1x' to each side of the equation. k + 4kx + 2kx2 + 1x + -1x + -1x2 = -3 + -1x Combine like terms: 1x + -1x = 0 k + 4kx + 2kx2 + 0 + -1x2 = -3 + -1x k + 4kx + 2kx2 + -1x2 = -3 + -1x Add 'x2' to each side of the equation. k + 4kx + 2kx2 + -1x2 + x2 = -3 + -1x + x2 Combine like terms: -1x2 + x2 = 0 k + 4kx + 2kx2 + 0 = -3 + -1x + x2 k + 4kx + 2kx2 = -3 + -1x + x2 Reorder the terms: 3 + k + 4kx + 2kx2 + x + -1x2 = -3 + -1x + x2 + 3 + x + -1x2 Reorder the terms: 3 + k + 4kx + 2kx2 + x + -1x2 = -3 + 3 + -1x + x + x2 + -1x2 Combine like terms: -3 + 3 = 0 3 + k + 4kx + 2kx2 + x + -1x2 = 0 + -1x + x + x2 + -1x2 3 + k + 4kx + 2kx2 + x + -1x2 = -1x + x + x2 + -1x2 Combine like terms: -1x + x = 0 3 + k + 4kx + 2kx2 + x + -1x2 = 0 + x2 + -1x2 3 + k + 4kx + 2kx2 + x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 3 + k + 4kx + 2kx2 + x + -1x2 = 0 The solution to this equation could not be determined.
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