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