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Simplifying 8x(8x) + 8x + 2 = 0 Remove parenthesis around (8x) 8x * 8x + 8x + 2 = 0 Reorder the terms for easier multiplication: 8 * 8x * x + 8x + 2 = 0 Multiply 8 * 8 64x * x + 8x + 2 = 0 Multiply x * x 64x2 + 8x + 2 = 0 Reorder the terms: 2 + 8x + 64x2 = 0 Solving 2 + 8x + 64x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(1 + 4x + 32x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + 4x + 32x2)' equal to zero and attempt to solve: Simplifying 1 + 4x + 32x2 = 0 Solving 1 + 4x + 32x2 = 0 Begin completing the square. Divide all terms by 32 the coefficient of the squared term: Divide each side by '32'. 0.03125 + 0.125x + x2 = 0 Move the constant term to the right: Add '-0.03125' to each side of the equation. 0.03125 + 0.125x + -0.03125 + x2 = 0 + -0.03125 Reorder the terms: 0.03125 + -0.03125 + 0.125x + x2 = 0 + -0.03125 Combine like terms: 0.03125 + -0.03125 = 0.00000 0.00000 + 0.125x + x2 = 0 + -0.03125 0.125x + x2 = 0 + -0.03125 Combine like terms: 0 + -0.03125 = -0.03125 0.125x + x2 = -0.03125 The x term is 0.125x. Take half its coefficient (0.0625). Square it (0.00390625) and add it to both sides. Add '0.00390625' to each side of the equation. 0.125x + 0.00390625 + x2 = -0.03125 + 0.00390625 Reorder the terms: 0.00390625 + 0.125x + x2 = -0.03125 + 0.00390625 Combine like terms: -0.03125 + 0.00390625 = -0.02734375 0.00390625 + 0.125x + x2 = -0.02734375 Factor a perfect square on the left side: (x + 0.0625)(x + 0.0625) = -0.02734375 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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