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Simplifying (4x + 1)(4x + 1) = -1 Reorder the terms: (1 + 4x)(4x + 1) = -1 Reorder the terms: (1 + 4x)(1 + 4x) = -1 Multiply (1 + 4x) * (1 + 4x) (1(1 + 4x) + 4x * (1 + 4x)) = -1 ((1 * 1 + 4x * 1) + 4x * (1 + 4x)) = -1 ((1 + 4x) + 4x * (1 + 4x)) = -1 (1 + 4x + (1 * 4x + 4x * 4x)) = -1 (1 + 4x + (4x + 16x2)) = -1 Combine like terms: 4x + 4x = 8x (1 + 8x + 16x2) = -1 Solving 1 + 8x + 16x2 = -1 Solving for variable 'x'. Reorder the terms: 1 + 1 + 8x + 16x2 = -1 + 1 Combine like terms: 1 + 1 = 2 2 + 8x + 16x2 = -1 + 1 Combine like terms: -1 + 1 = 0 2 + 8x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(1 + 4x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + 4x + 8x2)' equal to zero and attempt to solve: Simplifying 1 + 4x + 8x2 = 0 Solving 1 + 4x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.125 + 0.5x + x2 = 0 Move the constant term to the right: Add '-0.125' to each side of the equation. 0.125 + 0.5x + -0.125 + x2 = 0 + -0.125 Reorder the terms: 0.125 + -0.125 + 0.5x + x2 = 0 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + 0.5x + x2 = 0 + -0.125 0.5x + x2 = 0 + -0.125 Combine like terms: 0 + -0.125 = -0.125 0.5x + x2 = -0.125 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = -0.125 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = -0.125 + 0.0625 Combine like terms: -0.125 + 0.0625 = -0.0625 0.0625 + 0.5x + x2 = -0.0625 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = -0.0625 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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