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Simplifying x2 + 2(k + -3) * x + (5k + -1) = 0 Reorder the terms: x2 + 2(-3 + k) * x + (5k + -1) = 0 Reorder the terms for easier multiplication: x2 + 2x(-3 + k) + (5k + -1) = 0 x2 + (-3 * 2x + k * 2x) + (5k + -1) = 0 Reorder the terms: x2 + (2kx + -6x) + (5k + -1) = 0 x2 + (2kx + -6x) + (5k + -1) = 0 Reorder the terms: x2 + 2kx + -6x + (-1 + 5k) = 0 Remove parenthesis around (-1 + 5k) x2 + 2kx + -6x + -1 + 5k = 0 Reorder the terms: -1 + 5k + 2kx + -6x + x2 = 0 Solving -1 + 5k + 2kx + -6x + x2 = 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 + 5k + 2kx + -6x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 5k + 2kx + -6x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 5k + 2kx + -6x + x2 = 0 + 1 5k + 2kx + -6x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 5k + 2kx + -6x + x2 = 1 Add '6x' to each side of the equation. 5k + 2kx + -6x + 6x + x2 = 1 + 6x Combine like terms: -6x + 6x = 0 5k + 2kx + 0 + x2 = 1 + 6x 5k + 2kx + x2 = 1 + 6x Add '-1x2' to each side of the equation. 5k + 2kx + x2 + -1x2 = 1 + 6x + -1x2 Combine like terms: x2 + -1x2 = 0 5k + 2kx + 0 = 1 + 6x + -1x2 5k + 2kx = 1 + 6x + -1x2 Reorder the terms: -1 + 5k + 2kx + -6x + x2 = 1 + 6x + -1x2 + -1 + -6x + x2 Reorder the terms: -1 + 5k + 2kx + -6x + x2 = 1 + -1 + 6x + -6x + -1x2 + x2 Combine like terms: 1 + -1 = 0 -1 + 5k + 2kx + -6x + x2 = 0 + 6x + -6x + -1x2 + x2 -1 + 5k + 2kx + -6x + x2 = 6x + -6x + -1x2 + x2 Combine like terms: 6x + -6x = 0 -1 + 5k + 2kx + -6x + x2 = 0 + -1x2 + x2 -1 + 5k + 2kx + -6x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -1 + 5k + 2kx + -6x + x2 = 0 The solution to this equation could not be determined.
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