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Simplifying 0 = 8(4x2 + x + 3) Reorder the terms: 0 = 8(3 + x + 4x2) 0 = (3 * 8 + x * 8 + 4x2 * 8) 0 = (24 + 8x + 32x2) Solving 0 = 24 + 8x + 32x2 Solving for variable 'x'. Combine like terms: 0 + -24 = -24 -24 + -8x + -32x2 = 24 + 8x + 32x2 + -24 + -8x + -32x2 Reorder the terms: -24 + -8x + -32x2 = 24 + -24 + 8x + -8x + 32x2 + -32x2 Combine like terms: 24 + -24 = 0 -24 + -8x + -32x2 = 0 + 8x + -8x + 32x2 + -32x2 -24 + -8x + -32x2 = 8x + -8x + 32x2 + -32x2 Combine like terms: 8x + -8x = 0 -24 + -8x + -32x2 = 0 + 32x2 + -32x2 -24 + -8x + -32x2 = 32x2 + -32x2 Combine like terms: 32x2 + -32x2 = 0 -24 + -8x + -32x2 = 0 Factor out the Greatest Common Factor (GCF), '-8'. -8(3 + x + 4x2) = 0 Ignore the factor -8.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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