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