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Simplifying (k + 1) * x2 + 2(k + 1) * x + (2k + 3) = 0 Reorder the terms: (1 + k) * x2 + 2(k + 1) * x + (2k + 3) = 0 Reorder the terms for easier multiplication: x2(1 + k) + 2(k + 1) * x + (2k + 3) = 0 (1 * x2 + k * x2) + 2(k + 1) * x + (2k + 3) = 0 Reorder the terms: (kx2 + 1x2) + 2(k + 1) * x + (2k + 3) = 0 (kx2 + 1x2) + 2(k + 1) * x + (2k + 3) = 0 Reorder the terms: kx2 + 1x2 + 2(1 + k) * x + (2k + 3) = 0 Reorder the terms for easier multiplication: kx2 + 1x2 + 2x(1 + k) + (2k + 3) = 0 kx2 + 1x2 + (1 * 2x + k * 2x) + (2k + 3) = 0 Reorder the terms: kx2 + 1x2 + (2kx + 2x) + (2k + 3) = 0 kx2 + 1x2 + (2kx + 2x) + (2k + 3) = 0 Reorder the terms: kx2 + 1x2 + 2kx + 2x + (3 + 2k) = 0 Remove parenthesis around (3 + 2k) kx2 + 1x2 + 2kx + 2x + 3 + 2k = 0 Reorder the terms: 3 + 2k + 2kx + kx2 + 2x + 1x2 = 0 Solving 3 + 2k + 2kx + kx2 + 2x + 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 + 2k + 2kx + kx2 + 2x + -3 + 1x2 = 0 + -3 Reorder the terms: 3 + -3 + 2k + 2kx + kx2 + 2x + 1x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2k + 2kx + kx2 + 2x + 1x2 = 0 + -3 2k + 2kx + kx2 + 2x + 1x2 = 0 + -3 Combine like terms: 0 + -3 = -3 2k + 2kx + kx2 + 2x + 1x2 = -3 Add '-2x' to each side of the equation. 2k + 2kx + kx2 + 2x + -2x + 1x2 = -3 + -2x Combine like terms: 2x + -2x = 0 2k + 2kx + kx2 + 0 + 1x2 = -3 + -2x 2k + 2kx + kx2 + 1x2 = -3 + -2x Add '-1x2' to each side of the equation. 2k + 2kx + kx2 + 1x2 + -1x2 = -3 + -2x + -1x2 Combine like terms: 1x2 + -1x2 = 0 2k + 2kx + kx2 + 0 = -3 + -2x + -1x2 2k + 2kx + kx2 = -3 + -2x + -1x2 Reorder the terms: 3 + 2k + 2kx + kx2 + 2x + x2 = -3 + -2x + -1x2 + 3 + 2x + x2 Reorder the terms: 3 + 2k + 2kx + kx2 + 2x + x2 = -3 + 3 + -2x + 2x + -1x2 + x2 Combine like terms: -3 + 3 = 0 3 + 2k + 2kx + kx2 + 2x + x2 = 0 + -2x + 2x + -1x2 + x2 3 + 2k + 2kx + kx2 + 2x + x2 = -2x + 2x + -1x2 + x2 Combine like terms: -2x + 2x = 0 3 + 2k + 2kx + kx2 + 2x + x2 = 0 + -1x2 + x2 3 + 2k + 2kx + kx2 + 2x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 3 + 2k + 2kx + kx2 + 2x + x2 = 0 The solution to this equation could not be determined.
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