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Simplifying x2 + (3k + 2) * x + 2(2k + 1) = x2 + (3k + 8) * x + -2(2k + -1) Reorder the terms: x2 + (2 + 3k) * x + 2(2k + 1) = x2 + (3k + 8) * x + -2(2k + -1) Reorder the terms for easier multiplication: x2 + x(2 + 3k) + 2(2k + 1) = x2 + (3k + 8) * x + -2(2k + -1) x2 + (2 * x + 3k * x) + 2(2k + 1) = x2 + (3k + 8) * x + -2(2k + -1) Reorder the terms: x2 + (3kx + 2x) + 2(2k + 1) = x2 + (3k + 8) * x + -2(2k + -1) x2 + (3kx + 2x) + 2(2k + 1) = x2 + (3k + 8) * x + -2(2k + -1) Reorder the terms: x2 + 3kx + 2x + 2(1 + 2k) = x2 + (3k + 8) * x + -2(2k + -1) x2 + 3kx + 2x + (1 * 2 + 2k * 2) = x2 + (3k + 8) * x + -2(2k + -1) x2 + 3kx + 2x + (2 + 4k) = x2 + (3k + 8) * x + -2(2k + -1) Reorder the terms: 2 + 4k + 3kx + 2x + x2 = x2 + (3k + 8) * x + -2(2k + -1) Reorder the terms: 2 + 4k + 3kx + 2x + x2 = x2 + (8 + 3k) * x + -2(2k + -1) Reorder the terms for easier multiplication: 2 + 4k + 3kx + 2x + x2 = x2 + x(8 + 3k) + -2(2k + -1) 2 + 4k + 3kx + 2x + x2 = x2 + (8 * x + 3k * x) + -2(2k + -1) Reorder the terms: 2 + 4k + 3kx + 2x + x2 = x2 + (3kx + 8x) + -2(2k + -1) 2 + 4k + 3kx + 2x + x2 = x2 + (3kx + 8x) + -2(2k + -1) Reorder the terms: 2 + 4k + 3kx + 2x + x2 = x2 + 3kx + 8x + -2(-1 + 2k) 2 + 4k + 3kx + 2x + x2 = x2 + 3kx + 8x + (-1 * -2 + 2k * -2) 2 + 4k + 3kx + 2x + x2 = x2 + 3kx + 8x + (2 + -4k) Reorder the terms: 2 + 4k + 3kx + 2x + x2 = 2 + -4k + 3kx + 8x + x2 Add '-2' to each side of the equation. 2 + 4k + 3kx + 2x + -2 + x2 = 2 + -4k + 3kx + 8x + -2 + x2 Reorder the terms: 2 + -2 + 4k + 3kx + 2x + x2 = 2 + -4k + 3kx + 8x + -2 + x2 Combine like terms: 2 + -2 = 0 0 + 4k + 3kx + 2x + x2 = 2 + -4k + 3kx + 8x + -2 + x2 4k + 3kx + 2x + x2 = 2 + -4k + 3kx + 8x + -2 + x2 Reorder the terms: 4k + 3kx + 2x + x2 = 2 + -2 + -4k + 3kx + 8x + x2 Combine like terms: 2 + -2 = 0 4k + 3kx + 2x + x2 = 0 + -4k + 3kx + 8x + x2 4k + 3kx + 2x + x2 = -4k + 3kx + 8x + x2 Add '-3kx' to each side of the equation. 4k + 3kx + 2x + -3kx + x2 = -4k + 3kx + 8x + -3kx + x2 Reorder the terms: 4k + 3kx + -3kx + 2x + x2 = -4k + 3kx + 8x + -3kx + x2 Combine like terms: 3kx + -3kx = 0 4k + 0 + 2x + x2 = -4k + 3kx + 8x + -3kx + x2 4k + 2x + x2 = -4k + 3kx + 8x + -3kx + x2 Reorder the terms: 4k + 2x + x2 = -4k + 3kx + -3kx + 8x + x2 Combine like terms: 3kx + -3kx = 0 4k + 2x + x2 = -4k + 0 + 8x + x2 4k + 2x + x2 = -4k + 8x + x2 Add '-1x2' to each side of the equation. 4k + 2x + x2 + -1x2 = -4k + 8x + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 4k + 2x + 0 = -4k + 8x + x2 + -1x2 4k + 2x = -4k + 8x + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 4k + 2x = -4k + 8x + 0 4k + 2x = -4k + 8x Solving 4k + 2x = -4k + 8x Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '4k' to each side of the equation. 4k + 4k + 2x = -4k + 4k + 8x Combine like terms: 4k + 4k = 8k 8k + 2x = -4k + 4k + 8x Combine like terms: -4k + 4k = 0 8k + 2x = 0 + 8x 8k + 2x = 8x Add '-2x' to each side of the equation. 8k + 2x + -2x = 8x + -2x Combine like terms: 2x + -2x = 0 8k + 0 = 8x + -2x 8k = 8x + -2x Combine like terms: 8x + -2x = 6x 8k = 6x Divide each side by '8'. k = 0.75x Simplifying k = 0.75x
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