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Simplifying 0 = 8x2 + 8x + 9 Reorder the terms: 0 = 9 + 8x + 8x2 Solving 0 = 9 + 8x + 8x2 Solving for variable 'x'. Combine like terms: 0 + -9 = -9 -9 + -8x + -8x2 = 9 + 8x + 8x2 + -9 + -8x + -8x2 Reorder the terms: -9 + -8x + -8x2 = 9 + -9 + 8x + -8x + 8x2 + -8x2 Combine like terms: 9 + -9 = 0 -9 + -8x + -8x2 = 0 + 8x + -8x + 8x2 + -8x2 -9 + -8x + -8x2 = 8x + -8x + 8x2 + -8x2 Combine like terms: 8x + -8x = 0 -9 + -8x + -8x2 = 0 + 8x2 + -8x2 -9 + -8x + -8x2 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 -9 + -8x + -8x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(9 + 8x + 8x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(9 + 8x + 8x2)' equal to zero and attempt to solve: Simplifying 9 + 8x + 8x2 = 0 Solving 9 + 8x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 1.125 + x + x2 = 0 Move the constant term to the right: Add '-1.125' to each side of the equation. 1.125 + x + -1.125 + x2 = 0 + -1.125 Reorder the terms: 1.125 + -1.125 + x + x2 = 0 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x + x2 = 0 + -1.125 x + x2 = 0 + -1.125 Combine like terms: 0 + -1.125 = -1.125 x + x2 = -1.125 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 = -1.125 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = -1.125 + 0.25 Combine like terms: -1.125 + 0.25 = -0.875 1.25 + x2 = -0.875 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -0.875 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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