(K+1)x^2-2(3k+1)x+8k+1=0 - Solution

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(K+1)x^2-2(3k+1)x+8k+1=0

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Solution for (K+1)x^2-2(3k+1)x+8k+1=0 equation:

Simplifying (K + 1) * x2 + -2(3k + 1) * x + 8k + 1 = 0 Reorder the terms: (1 + K) * x2 + -2(3k + 1) * x + 8k + 1 = 0 Reorder the terms for easier multiplication: x2(1 + K) + -2(3k + 1) * x + 8k + 1 = 0 (1 * x2 + K * x2) + -2(3k + 1) * x + 8k + 1 = 0 (1x2 + x2K) + -2(3k + 1) * x + 8k + 1 = 0 Reorder the terms: 1x2 + x2K + -2(1 + 3k) * x + 8k + 1 = 0 Reorder the terms for easier multiplication: 1x2 + x2K + -2x(1 + 3k) + 8k + 1 = 0 1x2 + x2K + (1 * -2x + 3k * -2x) + 8k + 1 = 0 Reorder the terms: 1x2 + x2K + (-6kx + -2x) + 8k + 1 = 0 1x2 + x2K + (-6kx + -2x) + 8k + 1 = 0 Reorder the terms: 1 + 8k + -6kx + -2x + 1x2 + x2K = 0 Solving 1 + 8k + -6kx + -2x + 1x2 + x2K = 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 + 8k + -6kx + -2x + 1x2 + -1 + x2K = 0 + -1 Reorder the terms: 1 + -1 + 8k + -6kx + -2x + 1x2 + x2K = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 8k + -6kx + -2x + 1x2 + x2K = 0 + -1 8k + -6kx + -2x + 1x2 + x2K = 0 + -1 Combine like terms: 0 + -1 = -1 8k + -6kx + -2x + 1x2 + x2K = -1 Add '2x' to each side of the equation. 8k + -6kx + -2x + 1x2 + 2x + x2K = -1 + 2x Reorder the terms: 8k + -6kx + -2x + 2x + 1x2 + x2K = -1 + 2x Combine like terms: -2x + 2x = 0 8k + -6kx + 0 + 1x2 + x2K = -1 + 2x 8k + -6kx + 1x2 + x2K = -1 + 2x Add '-1x2' to each side of the equation. 8k + -6kx + 1x2 + -1x2 + x2K = -1 + 2x + -1x2 Combine like terms: 1x2 + -1x2 = 0 8k + -6kx + 0 + x2K = -1 + 2x + -1x2 8k + -6kx + x2K = -1 + 2x + -1x2 Add '-1x2K' to each side of the equation. 8k + -6kx + x2K + -1x2K = -1 + 2x + -1x2 + -1x2K Combine like terms: x2K + -1x2K = 0 8k + -6kx + 0 = -1 + 2x + -1x2 + -1x2K 8k + -6kx = -1 + 2x + -1x2 + -1x2K Reorder the terms: 1 + 8k + -6kx + -2x + x2 + x2K = -1 + 2x + -1x2 + -1x2K + 1 + -2x + x2 + x2K Reorder the terms: 1 + 8k + -6kx + -2x + x2 + x2K = -1 + 1 + 2x + -2x + -1x2 + x2 + -1x2K + x2K Combine like terms: -1 + 1 = 0 1 + 8k + -6kx + -2x + x2 + x2K = 0 + 2x + -2x + -1x2 + x2 + -1x2K + x2K 1 + 8k + -6kx + -2x + x2 + x2K = 2x + -2x + -1x2 + x2 + -1x2K + x2K Combine like terms: 2x + -2x = 0 1 + 8k + -6kx + -2x + x2 + x2K = 0 + -1x2 + x2 + -1x2K + x2K 1 + 8k + -6kx + -2x + x2 + x2K = -1x2 + x2 + -1x2K + x2K Combine like terms: -1x2 + x2 = 0 1 + 8k + -6kx + -2x + x2 + x2K = 0 + -1x2K + x2K 1 + 8k + -6kx + -2x + x2 + x2K = -1x2K + x2K Combine like terms: -1x2K + x2K = 0 1 + 8k + -6kx + -2x + x2 + x2K = 0 The solution to this equation could not be determined.

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