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Simplifying 0 = 8x2 + x + 12 Reorder the terms: 0 = 12 + x + 8x2 Solving 0 = 12 + x + 8x2 Solving for variable 'x'. Combine like terms: 0 + -12 = -12 -12 + -1x + -8x2 = 12 + x + 8x2 + -12 + -1x + -8x2 Reorder the terms: -12 + -1x + -8x2 = 12 + -12 + x + -1x + 8x2 + -8x2 Combine like terms: 12 + -12 = 0 -12 + -1x + -8x2 = 0 + x + -1x + 8x2 + -8x2 -12 + -1x + -8x2 = x + -1x + 8x2 + -8x2 Combine like terms: x + -1x = 0 -12 + -1x + -8x2 = 0 + 8x2 + -8x2 -12 + -1x + -8x2 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 -12 + -1x + -8x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(12 + x + 8x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(12 + x + 8x2)' equal to zero and attempt to solve: Simplifying 12 + x + 8x2 = 0 Solving 12 + x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 1.5 + 0.125x + x2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + 0.125x + -1.5 + x2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + 0.125x + x2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + 0.125x + x2 = 0 + -1.5 0.125x + x2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 0.125x + x2 = -1.5 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. 0.125x + 0.25 + x2 = -1.5 + 0.25 Reorder the terms: 0.25 + 0.125x + x2 = -1.5 + 0.25 Combine like terms: -1.5 + 0.25 = -1.25 0.25 + 0.125x + x2 = -1.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -1.25 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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