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Simplifying (x + 1)(x2 + kx + 4) = 0 Reorder the terms: (1 + x)(x2 + kx + 4) = 0 Reorder the terms: (1 + x)(4 + kx + x2) = 0 Multiply (1 + x) * (4 + kx + x2) (1(4 + kx + x2) + x(4 + kx + x2)) = 0 ((4 * 1 + kx * 1 + x2 * 1) + x(4 + kx + x2)) = 0 ((4 + 1kx + 1x2) + x(4 + kx + x2)) = 0 (4 + 1kx + 1x2 + (4 * x + kx * x + x2 * x)) = 0 Reorder the terms: (4 + 1kx + 1x2 + (kx2 + 4x + x3)) = 0 (4 + 1kx + 1x2 + (kx2 + 4x + x3)) = 0 Reorder the terms: (4 + 1kx + kx2 + 4x + 1x2 + x3) = 0 (4 + 1kx + kx2 + 4x + 1x2 + x3) = 0 Solving 4 + 1kx + kx2 + 4x + 1x2 + x3 = 0 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + 1kx + kx2 + 4x + 1x2 + -4 + x3 = 0 + -4 Reorder the terms: 4 + -4 + 1kx + kx2 + 4x + 1x2 + x3 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 1kx + kx2 + 4x + 1x2 + x3 = 0 + -4 1kx + kx2 + 4x + 1x2 + x3 = 0 + -4 Combine like terms: 0 + -4 = -4 1kx + kx2 + 4x + 1x2 + x3 = -4 Add '-4x' to each side of the equation. 1kx + kx2 + 4x + 1x2 + -4x + x3 = -4 + -4x Reorder the terms: 1kx + kx2 + 4x + -4x + 1x2 + x3 = -4 + -4x Combine like terms: 4x + -4x = 0 1kx + kx2 + 0 + 1x2 + x3 = -4 + -4x 1kx + kx2 + 1x2 + x3 = -4 + -4x Add '-1x2' to each side of the equation. 1kx + kx2 + 1x2 + -1x2 + x3 = -4 + -4x + -1x2 Combine like terms: 1x2 + -1x2 = 0 1kx + kx2 + 0 + x3 = -4 + -4x + -1x2 1kx + kx2 + x3 = -4 + -4x + -1x2 Add '-1x3' to each side of the equation. 1kx + kx2 + x3 + -1x3 = -4 + -4x + -1x2 + -1x3 Combine like terms: x3 + -1x3 = 0 1kx + kx2 + 0 = -4 + -4x + -1x2 + -1x3 1kx + kx2 = -4 + -4x + -1x2 + -1x3 Reorder the terms: 4 + 1kx + kx2 + 4x + x2 + x3 = -4 + -4x + -1x2 + -1x3 + 4 + 4x + x2 + x3 Reorder the terms: 4 + 1kx + kx2 + 4x + x2 + x3 = -4 + 4 + -4x + 4x + -1x2 + x2 + -1x3 + x3 Combine like terms: -4 + 4 = 0 4 + 1kx + kx2 + 4x + x2 + x3 = 0 + -4x + 4x + -1x2 + x2 + -1x3 + x3 4 + 1kx + kx2 + 4x + x2 + x3 = -4x + 4x + -1x2 + x2 + -1x3 + x3 Combine like terms: -4x + 4x = 0 4 + 1kx + kx2 + 4x + x2 + x3 = 0 + -1x2 + x2 + -1x3 + x3 4 + 1kx + kx2 + 4x + x2 + x3 = -1x2 + x2 + -1x3 + x3 Combine like terms: -1x2 + x2 = 0 4 + 1kx + kx2 + 4x + x2 + x3 = 0 + -1x3 + x3 4 + 1kx + kx2 + 4x + x2 + x3 = -1x3 + x3 Combine like terms: -1x3 + x3 = 0 4 + 1kx + kx2 + 4x + x2 + x3 = 0 The solution to this equation could not be determined.
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