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Simplifying -8x2 + -8x + -67 = 0 Reorder the terms: -67 + -8x + -8x2 = 0 Solving -67 + -8x + -8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(67 + 8x + 8x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(67 + 8x + 8x2)' equal to zero and attempt to solve: Simplifying 67 + 8x + 8x2 = 0 Solving 67 + 8x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 8.375 + x + x2 = 0 Move the constant term to the right: Add '-8.375' to each side of the equation. 8.375 + x + -8.375 + x2 = 0 + -8.375 Reorder the terms: 8.375 + -8.375 + x + x2 = 0 + -8.375 Combine like terms: 8.375 + -8.375 = 0.000 0.000 + x + x2 = 0 + -8.375 x + x2 = 0 + -8.375 Combine like terms: 0 + -8.375 = -8.375 x + x2 = -8.375 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. + 0.25 + x2 = -8.375 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = -8.375 + 0.25 Combine like terms: -8.375 + 0.25 = -8.125 1.25 + x2 = -8.125 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -8.125 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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