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Simplifying 8x2 + 2x + 6 = 0 Reorder the terms: 6 + 2x + 8x2 = 0 Solving 6 + 2x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(3 + x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + x + 4x2)' equal to zero and attempt to solve: Simplifying 3 + x + 4x2 = 0 Solving 3 + x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.75 + 0.25x + x2 = 0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + 0.25x + -0.75 + x2 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + 0.25x + x2 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + 0.25x + x2 = 0 + -0.75 0.25x + x2 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 0.25x + x2 = -0.75 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.25x + 0.25 + x2 = -0.75 + 0.25 Reorder the terms: 0.25 + 0.25x + x2 = -0.75 + 0.25 Combine like terms: -0.75 + 0.25 = -0.5 0.25 + 0.25x + x2 = -0.5 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -0.5 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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