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Simplifying x2 + (3k + 1) * x + 8 = 0 Reorder the terms: x2 + (1 + 3k) * x + 8 = 0 Reorder the terms for easier multiplication: x2 + x(1 + 3k) + 8 = 0 x2 + (1 * x + 3k * x) + 8 = 0 Reorder the terms: x2 + (3kx + 1x) + 8 = 0 x2 + (3kx + 1x) + 8 = 0 Reorder the terms: 8 + 3kx + 1x + x2 = 0 Solving 8 + 3kx + 1x + x2 = 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 + 3kx + 1x + -8 + x2 = 0 + -8 Reorder the terms: 8 + -8 + 3kx + 1x + x2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 3kx + 1x + x2 = 0 + -8 3kx + 1x + x2 = 0 + -8 Combine like terms: 0 + -8 = -8 3kx + 1x + x2 = -8 Add '-1x' to each side of the equation. 3kx + 1x + -1x + x2 = -8 + -1x Combine like terms: 1x + -1x = 0 3kx + 0 + x2 = -8 + -1x 3kx + x2 = -8 + -1x Add '-1x2' to each side of the equation. 3kx + x2 + -1x2 = -8 + -1x + -1x2 Combine like terms: x2 + -1x2 = 0 3kx + 0 = -8 + -1x + -1x2 3kx = -8 + -1x + -1x2 Divide each side by '3x'. k = -2.666666667x-1 + -0.3333333333 + -0.3333333333x Simplifying k = -2.666666667x-1 + -0.3333333333 + -0.3333333333x Reorder the terms: k = -0.3333333333 + -2.666666667x-1 + -0.3333333333x
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