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Simplifying x2 + 8(2K + -1) * x + 12(3K + 1) = 0 Reorder the terms: x2 + 8(-1 + 2K) * x + 12(3K + 1) = 0 Reorder the terms for easier multiplication: x2 + 8x(-1 + 2K) + 12(3K + 1) = 0 x2 + (-1 * 8x + 2K * 8x) + 12(3K + 1) = 0 x2 + (-8x + 16xK) + 12(3K + 1) = 0 Reorder the terms: x2 + -8x + 16xK + 12(1 + 3K) = 0 x2 + -8x + 16xK + (1 * 12 + 3K * 12) = 0 x2 + -8x + 16xK + (12 + 36K) = 0 Reorder the terms: 12 + 36K + -8x + 16xK + x2 = 0 Solving 12 + 36K + -8x + 16xK + x2 = 0 Solving for variable 'K'. Move all terms containing K to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + 36K + -8x + 16xK + -12 + x2 = 0 + -12 Reorder the terms: 12 + -12 + 36K + -8x + 16xK + x2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + 36K + -8x + 16xK + x2 = 0 + -12 36K + -8x + 16xK + x2 = 0 + -12 Combine like terms: 0 + -12 = -12 36K + -8x + 16xK + x2 = -12 Add '8x' to each side of the equation. 36K + -8x + 16xK + 8x + x2 = -12 + 8x Reorder the terms: 36K + -8x + 8x + 16xK + x2 = -12 + 8x Combine like terms: -8x + 8x = 0 36K + 0 + 16xK + x2 = -12 + 8x 36K + 16xK + x2 = -12 + 8x Add '-1x2' to each side of the equation. 36K + 16xK + x2 + -1x2 = -12 + 8x + -1x2 Combine like terms: x2 + -1x2 = 0 36K + 16xK + 0 = -12 + 8x + -1x2 36K + 16xK = -12 + 8x + -1x2 Reorder the terms: 12 + 36K + -8x + 16xK + x2 = -12 + 8x + -1x2 + 12 + -8x + x2 Reorder the terms: 12 + 36K + -8x + 16xK + x2 = -12 + 12 + 8x + -8x + -1x2 + x2 Combine like terms: -12 + 12 = 0 12 + 36K + -8x + 16xK + x2 = 0 + 8x + -8x + -1x2 + x2 12 + 36K + -8x + 16xK + x2 = 8x + -8x + -1x2 + x2 Combine like terms: 8x + -8x = 0 12 + 36K + -8x + 16xK + x2 = 0 + -1x2 + x2 12 + 36K + -8x + 16xK + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 12 + 36K + -8x + 16xK + x2 = 0 The solution to this equation could not be determined.
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