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Simplifying (k + 1) * x2 + (4k + 1) * x + (k + -5) = 0 Reorder the terms: (1 + k) * x2 + (4k + 1) * x + (k + -5) = 0 Reorder the terms for easier multiplication: x2(1 + k) + (4k + 1) * x + (k + -5) = 0 (1 * x2 + k * x2) + (4k + 1) * x + (k + -5) = 0 Reorder the terms: (kx2 + 1x2) + (4k + 1) * x + (k + -5) = 0 (kx2 + 1x2) + (4k + 1) * x + (k + -5) = 0 Reorder the terms: kx2 + 1x2 + (1 + 4k) * x + (k + -5) = 0 Reorder the terms for easier multiplication: kx2 + 1x2 + x(1 + 4k) + (k + -5) = 0 kx2 + 1x2 + (1 * x + 4k * x) + (k + -5) = 0 Reorder the terms: kx2 + 1x2 + (4kx + 1x) + (k + -5) = 0 kx2 + 1x2 + (4kx + 1x) + (k + -5) = 0 Reorder the terms: kx2 + 1x2 + 4kx + 1x + (-5 + k) = 0 Remove parenthesis around (-5 + k) kx2 + 1x2 + 4kx + 1x + -5 + k = 0 Reorder the terms: -5 + k + 4kx + kx2 + 1x + 1x2 = 0 Solving -5 + k + 4kx + kx2 + 1x + 1x2 = 0 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '5' to each side of the equation. -5 + k + 4kx + kx2 + 1x + 5 + 1x2 = 0 + 5 Reorder the terms: -5 + 5 + k + 4kx + kx2 + 1x + 1x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + k + 4kx + kx2 + 1x + 1x2 = 0 + 5 k + 4kx + kx2 + 1x + 1x2 = 0 + 5 Combine like terms: 0 + 5 = 5 k + 4kx + kx2 + 1x + 1x2 = 5 Add '-1x' to each side of the equation. k + 4kx + kx2 + 1x + -1x + 1x2 = 5 + -1x Combine like terms: 1x + -1x = 0 k + 4kx + kx2 + 0 + 1x2 = 5 + -1x k + 4kx + kx2 + 1x2 = 5 + -1x Add '-1x2' to each side of the equation. k + 4kx + kx2 + 1x2 + -1x2 = 5 + -1x + -1x2 Combine like terms: 1x2 + -1x2 = 0 k + 4kx + kx2 + 0 = 5 + -1x + -1x2 k + 4kx + kx2 = 5 + -1x + -1x2 Reorder the terms: -5 + k + 4kx + kx2 + x + x2 = 5 + -1x + -1x2 + -5 + x + x2 Reorder the terms: -5 + k + 4kx + kx2 + x + x2 = 5 + -5 + -1x + x + -1x2 + x2 Combine like terms: 5 + -5 = 0 -5 + k + 4kx + kx2 + x + x2 = 0 + -1x + x + -1x2 + x2 -5 + k + 4kx + kx2 + x + x2 = -1x + x + -1x2 + x2 Combine like terms: -1x + x = 0 -5 + k + 4kx + kx2 + x + x2 = 0 + -1x2 + x2 -5 + k + 4kx + kx2 + x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -5 + k + 4kx + kx2 + x + x2 = 0 The solution to this equation could not be determined.
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