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Simplifying 5x + -1(4x + 1)(4x + 1) = 0 Reorder the terms: 5x + -1(1 + 4x)(4x + 1) = 0 Reorder the terms: 5x + -1(1 + 4x)(1 + 4x) = 0 Multiply (1 + 4x) * (1 + 4x) 5x + -1(1(1 + 4x) + 4x * (1 + 4x)) = 0 5x + -1((1 * 1 + 4x * 1) + 4x * (1 + 4x)) = 0 5x + -1((1 + 4x) + 4x * (1 + 4x)) = 0 5x + -1(1 + 4x + (1 * 4x + 4x * 4x)) = 0 5x + -1(1 + 4x + (4x + 16x2)) = 0 Combine like terms: 4x + 4x = 8x 5x + -1(1 + 8x + 16x2) = 0 5x + (1 * -1 + 8x * -1 + 16x2 * -1) = 0 5x + (-1 + -8x + -16x2) = 0 Reorder the terms: -1 + 5x + -8x + -16x2 = 0 Combine like terms: 5x + -8x = -3x -1 + -3x + -16x2 = 0 Solving -1 + -3x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(1 + 3x + 16x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(1 + 3x + 16x2)' equal to zero and attempt to solve: Simplifying 1 + 3x + 16x2 = 0 Solving 1 + 3x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.0625 + 0.1875x + x2 = 0 Move the constant term to the right: Add '-0.0625' to each side of the equation. 0.0625 + 0.1875x + -0.0625 + x2 = 0 + -0.0625 Reorder the terms: 0.0625 + -0.0625 + 0.1875x + x2 = 0 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 0.0000 + 0.1875x + x2 = 0 + -0.0625 0.1875x + x2 = 0 + -0.0625 Combine like terms: 0 + -0.0625 = -0.0625 0.1875x + x2 = -0.0625 The x term is 0.1875x. Take half its coefficient (0.09375). Square it (0.0087890625) and add it to both sides. Add '0.0087890625' to each side of the equation. 0.1875x + 0.0087890625 + x2 = -0.0625 + 0.0087890625 Reorder the terms: 0.0087890625 + 0.1875x + x2 = -0.0625 + 0.0087890625 Combine like terms: -0.0625 + 0.0087890625 = -0.0537109375 0.0087890625 + 0.1875x + x2 = -0.0537109375 Factor a perfect square on the left side: (x + 0.09375)(x + 0.09375) = -0.0537109375 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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