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Simplifying 6x = 16x2 + -2x + 6 Reorder the terms: 6x = 6 + -2x + 16x2 Solving 6x = 6 + -2x + 16x2 Solving for variable 'x'. Reorder the terms: -6 + 6x + 2x + -16x2 = 6 + -2x + 16x2 + -6 + 2x + -16x2 Combine like terms: 6x + 2x = 8x -6 + 8x + -16x2 = 6 + -2x + 16x2 + -6 + 2x + -16x2 Reorder the terms: -6 + 8x + -16x2 = 6 + -6 + -2x + 2x + 16x2 + -16x2 Combine like terms: 6 + -6 = 0 -6 + 8x + -16x2 = 0 + -2x + 2x + 16x2 + -16x2 -6 + 8x + -16x2 = -2x + 2x + 16x2 + -16x2 Combine like terms: -2x + 2x = 0 -6 + 8x + -16x2 = 0 + 16x2 + -16x2 -6 + 8x + -16x2 = 16x2 + -16x2 Combine like terms: 16x2 + -16x2 = 0 -6 + 8x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + 4x + -8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + 4x + -8x2)' equal to zero and attempt to solve: Simplifying -3 + 4x + -8x2 = 0 Solving -3 + 4x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. 0.375 + -0.5x + x2 = 0 Move the constant term to the right: Add '-0.375' to each side of the equation. 0.375 + -0.5x + -0.375 + x2 = 0 + -0.375 Reorder the terms: 0.375 + -0.375 + -0.5x + x2 = 0 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + -0.5x + x2 = 0 + -0.375 -0.5x + x2 = 0 + -0.375 Combine like terms: 0 + -0.375 = -0.375 -0.5x + x2 = -0.375 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 = -0.375 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = -0.375 + 0.0625 Combine like terms: -0.375 + 0.0625 = -0.3125 0.0625 + -0.5x + x2 = -0.3125 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = -0.3125 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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