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Simplifying -6a2 + -1a + -5 = 0 Reorder the terms: -5 + -1a + -6a2 = 0 Solving -5 + -1a + -6a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '-1'. -1(5 + a + 6a2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(5 + a + 6a2)' equal to zero and attempt to solve: Simplifying 5 + a + 6a2 = 0 Solving 5 + a + 6a2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.8333333333 + 0.1666666667a + a2 = 0 Move the constant term to the right: Add '-0.8333333333' to each side of the equation. 0.8333333333 + 0.1666666667a + -0.8333333333 + a2 = 0 + -0.8333333333 Reorder the terms: 0.8333333333 + -0.8333333333 + 0.1666666667a + a2 = 0 + -0.8333333333 Combine like terms: 0.8333333333 + -0.8333333333 = 0.0000000000 0.0000000000 + 0.1666666667a + a2 = 0 + -0.8333333333 0.1666666667a + a2 = 0 + -0.8333333333 Combine like terms: 0 + -0.8333333333 = -0.8333333333 0.1666666667a + a2 = -0.8333333333 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. 0.1666666667a + 0.25 + a2 = -0.8333333333 + 0.25 Reorder the terms: 0.25 + 0.1666666667a + a2 = -0.8333333333 + 0.25 Combine like terms: -0.8333333333 + 0.25 = -0.5833333333 0.25 + 0.1666666667a + a2 = -0.5833333333 Factor a perfect square on the left side: (a + 0.5)(a + 0.5) = -0.5833333333 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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