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Simplifying (4x + 2)(4x + 2) + 1 = 0 Reorder the terms: (2 + 4x)(4x + 2) + 1 = 0 Reorder the terms: (2 + 4x)(2 + 4x) + 1 = 0 Multiply (2 + 4x) * (2 + 4x) (2(2 + 4x) + 4x * (2 + 4x)) + 1 = 0 ((2 * 2 + 4x * 2) + 4x * (2 + 4x)) + 1 = 0 ((4 + 8x) + 4x * (2 + 4x)) + 1 = 0 (4 + 8x + (2 * 4x + 4x * 4x)) + 1 = 0 (4 + 8x + (8x + 16x2)) + 1 = 0 Combine like terms: 8x + 8x = 16x (4 + 16x + 16x2) + 1 = 0 Reorder the terms: 4 + 1 + 16x + 16x2 = 0 Combine like terms: 4 + 1 = 5 5 + 16x + 16x2 = 0 Solving 5 + 16x + 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'. 0.3125 + x + x2 = 0 Move the constant term to the right: Add '-0.3125' to each side of the equation. 0.3125 + x + -0.3125 + x2 = 0 + -0.3125 Reorder the terms: 0.3125 + -0.3125 + x + x2 = 0 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + x + x2 = 0 + -0.3125 x + x2 = 0 + -0.3125 Combine like terms: 0 + -0.3125 = -0.3125 x + x2 = -0.3125 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = -0.3125 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = -0.3125 + 0.25 Combine like terms: -0.3125 + 0.25 = -0.0625 1.25 + x2 = -0.0625 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -0.0625 Can't calculate square root of the right side. The solution to this equation could not be determined.
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