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Simplifying (k + 5) * x2 + 3x + -1 = 0 Reorder the terms: (5 + k) * x2 + 3x + -1 = 0 Reorder the terms for easier multiplication: x2(5 + k) + 3x + -1 = 0 (5 * x2 + k * x2) + 3x + -1 = 0 Reorder the terms: (kx2 + 5x2) + 3x + -1 = 0 (kx2 + 5x2) + 3x + -1 = 0 Reorder the terms: -1 + kx2 + 3x + 5x2 = 0 Solving -1 + kx2 + 3x + 5x2 = 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 + kx2 + 3x + 1 + 5x2 = 0 + 1 Reorder the terms: -1 + 1 + kx2 + 3x + 5x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + kx2 + 3x + 5x2 = 0 + 1 kx2 + 3x + 5x2 = 0 + 1 Combine like terms: 0 + 1 = 1 kx2 + 3x + 5x2 = 1 Add '-3x' to each side of the equation. kx2 + 3x + -3x + 5x2 = 1 + -3x Combine like terms: 3x + -3x = 0 kx2 + 0 + 5x2 = 1 + -3x kx2 + 5x2 = 1 + -3x Add '-5x2' to each side of the equation. kx2 + 5x2 + -5x2 = 1 + -3x + -5x2 Combine like terms: 5x2 + -5x2 = 0 kx2 + 0 = 1 + -3x + -5x2 kx2 = 1 + -3x + -5x2 Divide each side by 'x2'. k = x-2 + -3x-1 + -5 Simplifying k = x-2 + -3x-1 + -5 Reorder the terms: k = -5 + x-2 + -3x-1
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