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