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Simplifying 2x2 + (k + 1) * x + 18 = 0 Reorder the terms: 2x2 + (1 + k) * x + 18 = 0 Reorder the terms for easier multiplication: 2x2 + x(1 + k) + 18 = 0 2x2 + (1 * x + k * x) + 18 = 0 Reorder the terms: 2x2 + (kx + 1x) + 18 = 0 2x2 + (kx + 1x) + 18 = 0 Reorder the terms: 18 + kx + 1x + 2x2 = 0 Solving 18 + kx + 1x + 2x2 = 0 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + kx + 1x + -18 + 2x2 = 0 + -18 Reorder the terms: 18 + -18 + kx + 1x + 2x2 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + kx + 1x + 2x2 = 0 + -18 kx + 1x + 2x2 = 0 + -18 Combine like terms: 0 + -18 = -18 kx + 1x + 2x2 = -18 Add '-1x' to each side of the equation. kx + 1x + -1x + 2x2 = -18 + -1x Combine like terms: 1x + -1x = 0 kx + 0 + 2x2 = -18 + -1x kx + 2x2 = -18 + -1x Add '-2x2' to each side of the equation. kx + 2x2 + -2x2 = -18 + -1x + -2x2 Combine like terms: 2x2 + -2x2 = 0 kx + 0 = -18 + -1x + -2x2 kx = -18 + -1x + -2x2 Divide each side by 'x'. k = -18x-1 + -1 + -2x Simplifying k = -18x-1 + -1 + -2x Reorder the terms: k = -1 + -18x-1 + -2x
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