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Simplifying (1 + -2x) * 2 + -1(1 + 4x)(1 + -4x) = 0 Reorder the terms for easier multiplication: 2(1 + -2x) + -1(1 + 4x)(1 + -4x) = 0 (1 * 2 + -2x * 2) + -1(1 + 4x)(1 + -4x) = 0 (2 + -4x) + -1(1 + 4x)(1 + -4x) = 0 Multiply (1 + 4x) * (1 + -4x) 2 + -4x + -1(1(1 + -4x) + 4x * (1 + -4x)) = 0 2 + -4x + -1((1 * 1 + -4x * 1) + 4x * (1 + -4x)) = 0 2 + -4x + -1((1 + -4x) + 4x * (1 + -4x)) = 0 2 + -4x + -1(1 + -4x + (1 * 4x + -4x * 4x)) = 0 2 + -4x + -1(1 + -4x + (4x + -16x2)) = 0 Combine like terms: -4x + 4x = 0 2 + -4x + -1(1 + 0 + -16x2) = 0 2 + -4x + -1(1 + -16x2) = 0 2 + -4x + (1 * -1 + -16x2 * -1) = 0 2 + -4x + (-1 + 16x2) = 0 Reorder the terms: 2 + -1 + -4x + 16x2 = 0 Combine like terms: 2 + -1 = 1 1 + -4x + 16x2 = 0 Solving 1 + -4x + 16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.0625 + -0.25x + x2 = 0 Move the constant term to the right: Add '-0.0625' to each side of the equation. 0.0625 + -0.25x + -0.0625 + x2 = 0 + -0.0625 Reorder the terms: 0.0625 + -0.0625 + -0.25x + x2 = 0 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 0.0000 + -0.25x + x2 = 0 + -0.0625 -0.25x + x2 = 0 + -0.0625 Combine like terms: 0 + -0.0625 = -0.0625 -0.25x + x2 = -0.0625 The x term is -0.25x. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25x + 0.015625 + x2 = -0.0625 + 0.015625 Reorder the terms: 0.015625 + -0.25x + x2 = -0.0625 + 0.015625 Combine like terms: -0.0625 + 0.015625 = -0.046875 0.015625 + -0.25x + x2 = -0.046875 Factor a perfect square on the left side: (x + -0.125)(x + -0.125) = -0.046875 Can't calculate square root of the right side. The solution to this equation could not be determined.
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