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Simplifying (k + 1) * x2 + 5x + 2 = 0 Reorder the terms: (1 + k) * x2 + 5x + 2 = 0 Reorder the terms for easier multiplication: x2(1 + k) + 5x + 2 = 0 (1 * x2 + k * x2) + 5x + 2 = 0 Reorder the terms: (kx2 + 1x2) + 5x + 2 = 0 (kx2 + 1x2) + 5x + 2 = 0 Reorder the terms: 2 + kx2 + 5x + 1x2 = 0 Solving 2 + kx2 + 5x + 1x2 = 0 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + kx2 + 5x + -2 + 1x2 = 0 + -2 Reorder the terms: 2 + -2 + kx2 + 5x + 1x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + kx2 + 5x + 1x2 = 0 + -2 kx2 + 5x + 1x2 = 0 + -2 Combine like terms: 0 + -2 = -2 kx2 + 5x + 1x2 = -2 Add '-5x' to each side of the equation. kx2 + 5x + -5x + 1x2 = -2 + -5x Combine like terms: 5x + -5x = 0 kx2 + 0 + 1x2 = -2 + -5x kx2 + 1x2 = -2 + -5x Add '-1x2' to each side of the equation. kx2 + 1x2 + -1x2 = -2 + -5x + -1x2 Combine like terms: 1x2 + -1x2 = 0 kx2 + 0 = -2 + -5x + -1x2 kx2 = -2 + -5x + -1x2 Divide each side by 'x2'. k = -2x-2 + -5x-1 + -1 Simplifying k = -2x-2 + -5x-1 + -1 Reorder the terms: k = -1 + -2x-2 + -5x-1
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