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Simplifying (2k + 1) * x2 + -6x + 1 = 0 Reorder the terms: (1 + 2k) * x2 + -6x + 1 = 0 Reorder the terms for easier multiplication: x2(1 + 2k) + -6x + 1 = 0 (1 * x2 + 2k * x2) + -6x + 1 = 0 Reorder the terms: (2kx2 + 1x2) + -6x + 1 = 0 (2kx2 + 1x2) + -6x + 1 = 0 Reorder the terms: 1 + 2kx2 + -6x + 1x2 = 0 Solving 1 + 2kx2 + -6x + 1x2 = 0 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + 2kx2 + -6x + -1 + 1x2 = 0 + -1 Reorder the terms: 1 + -1 + 2kx2 + -6x + 1x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2kx2 + -6x + 1x2 = 0 + -1 2kx2 + -6x + 1x2 = 0 + -1 Combine like terms: 0 + -1 = -1 2kx2 + -6x + 1x2 = -1 Add '6x' to each side of the equation. 2kx2 + -6x + 6x + 1x2 = -1 + 6x Combine like terms: -6x + 6x = 0 2kx2 + 0 + 1x2 = -1 + 6x 2kx2 + 1x2 = -1 + 6x Add '-1x2' to each side of the equation. 2kx2 + 1x2 + -1x2 = -1 + 6x + -1x2 Combine like terms: 1x2 + -1x2 = 0 2kx2 + 0 = -1 + 6x + -1x2 2kx2 = -1 + 6x + -1x2 Divide each side by '2x2'. k = -0.5x-2 + 3x-1 + -0.5 Simplifying k = -0.5x-2 + 3x-1 + -0.5 Reorder the terms: k = -0.5 + -0.5x-2 + 3x-1
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