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Simplifying 16x2 + 4x + 6 = 0 Reorder the terms: 6 + 4x + 16x2 = 0 Solving 6 + 4x + 16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(3 + 2x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + 2x + 8x2)' equal to zero and attempt to solve: Simplifying 3 + 2x + 8x2 = 0 Solving 3 + 2x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.375 + 0.25x + x2 = 0 Move the constant term to the right: Add '-0.375' to each side of the equation. 0.375 + 0.25x + -0.375 + x2 = 0 + -0.375 Reorder the terms: 0.375 + -0.375 + 0.25x + x2 = 0 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + 0.25x + x2 = 0 + -0.375 0.25x + x2 = 0 + -0.375 Combine like terms: 0 + -0.375 = -0.375 0.25x + x2 = -0.375 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 = -0.375 + 0.015625 Reorder the terms: 0.015625 + 0.25x + x2 = -0.375 + 0.015625 Combine like terms: -0.375 + 0.015625 = -0.359375 0.015625 + 0.25x + x2 = -0.359375 Factor a perfect square on the left side: (x + 0.125)(x + 0.125) = -0.359375 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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