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Simplifying 4kx2 + -2(K + 1) * x + 1 = 0 Reorder the terms: 4kx2 + -2(1 + K) * x + 1 = 0 Reorder the terms for easier multiplication: 4kx2 + -2x(1 + K) + 1 = 0 4kx2 + (1 * -2x + K * -2x) + 1 = 0 4kx2 + (-2x + -2xK) + 1 = 0 Reorder the terms: 1 + 4kx2 + -2x + -2xK = 0 Solving 1 + 4kx2 + -2x + -2xK = 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 + 4kx2 + -2x + -1 + -2xK = 0 + -1 Reorder the terms: 1 + -1 + 4kx2 + -2x + -2xK = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4kx2 + -2x + -2xK = 0 + -1 4kx2 + -2x + -2xK = 0 + -1 Combine like terms: 0 + -1 = -1 4kx2 + -2x + -2xK = -1 Add '2x' to each side of the equation. 4kx2 + -2x + 2x + -2xK = -1 + 2x Combine like terms: -2x + 2x = 0 4kx2 + 0 + -2xK = -1 + 2x 4kx2 + -2xK = -1 + 2x Add '2xK' to each side of the equation. 4kx2 + -2xK + 2xK = -1 + 2x + 2xK Combine like terms: -2xK + 2xK = 0 4kx2 + 0 = -1 + 2x + 2xK 4kx2 = -1 + 2x + 2xK Divide each side by '4x2'. k = -0.25x-2 + 0.5x-1 + 0.5x-1K Simplifying k = -0.25x-2 + 0.5x-1 + 0.5x-1K
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