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Simplifying (3k + 1) * x2 + 2x = 1 Reorder the terms: (1 + 3k) * x2 + 2x = 1 Reorder the terms for easier multiplication: x2(1 + 3k) + 2x = 1 (1 * x2 + 3k * x2) + 2x = 1 Reorder the terms: (3kx2 + 1x2) + 2x = 1 (3kx2 + 1x2) + 2x = 1 Reorder the terms: 3kx2 + 2x + 1x2 = 1 Solving 3kx2 + 2x + 1x2 = 1 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-2x' to each side of the equation. 3kx2 + 2x + -2x + 1x2 = 1 + -2x Combine like terms: 2x + -2x = 0 3kx2 + 0 + 1x2 = 1 + -2x 3kx2 + 1x2 = 1 + -2x Add '-1x2' to each side of the equation. 3kx2 + 1x2 + -1x2 = 1 + -2x + -1x2 Combine like terms: 1x2 + -1x2 = 0 3kx2 + 0 = 1 + -2x + -1x2 3kx2 = 1 + -2x + -1x2 Divide each side by '3x2'. k = 0.3333333333x-2 + -0.6666666667x-1 + -0.3333333333 Simplifying k = 0.3333333333x-2 + -0.6666666667x-1 + -0.3333333333 Reorder the terms: k = -0.3333333333 + 0.3333333333x-2 + -0.6666666667x-1
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