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Simplifying -9a2 + -1a + 2 = 8 Reorder the terms: 2 + -1a + -9a2 = 8 Solving 2 + -1a + -9a2 = 8 Solving for variable 'a'. Reorder the terms: 2 + -8 + -1a + -9a2 = 8 + -8 Combine like terms: 2 + -8 = -6 -6 + -1a + -9a2 = 8 + -8 Combine like terms: 8 + -8 = 0 -6 + -1a + -9a2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(6 + a + 9a2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(6 + a + 9a2)' equal to zero and attempt to solve: Simplifying 6 + a + 9a2 = 0 Solving 6 + a + 9a2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.6666666667 + 0.1111111111a + a2 = 0 Move the constant term to the right: Add '-0.6666666667' to each side of the equation. 0.6666666667 + 0.1111111111a + -0.6666666667 + a2 = 0 + -0.6666666667 Reorder the terms: 0.6666666667 + -0.6666666667 + 0.1111111111a + a2 = 0 + -0.6666666667 Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000 0.0000000000 + 0.1111111111a + a2 = 0 + -0.6666666667 0.1111111111a + a2 = 0 + -0.6666666667 Combine like terms: 0 + -0.6666666667 = -0.6666666667 0.1111111111a + a2 = -0.6666666667 The a term is a. 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. 0.1111111111a + 0.25 + a2 = -0.6666666667 + 0.25 Reorder the terms: 0.25 + 0.1111111111a + a2 = -0.6666666667 + 0.25 Combine like terms: -0.6666666667 + 0.25 = -0.4166666667 0.25 + 0.1111111111a + a2 = -0.4166666667 Factor a perfect square on the left side: (a + 0.5)(a + 0.5) = -0.4166666667 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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