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Simplifying 6a2 + -3a + 24 = 0 Reorder the terms: 24 + -3a + 6a2 = 0 Solving 24 + -3a + 6a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '3'. 3(8 + -1a + 2a2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(8 + -1a + 2a2)' equal to zero and attempt to solve: Simplifying 8 + -1a + 2a2 = 0 Solving 8 + -1a + 2a2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 4 + -0.5a + a2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -0.5a + -4 + a2 = 0 + -4 Reorder the terms: 4 + -4 + -0.5a + a2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -0.5a + a2 = 0 + -4 -0.5a + a2 = 0 + -4 Combine like terms: 0 + -4 = -4 -0.5a + a2 = -4 The a term is -0.5a. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5a + 0.0625 + a2 = -4 + 0.0625 Reorder the terms: 0.0625 + -0.5a + a2 = -4 + 0.0625 Combine like terms: -4 + 0.0625 = -3.9375 0.0625 + -0.5a + a2 = -3.9375 Factor a perfect square on the left side: (a + -0.25)(a + -0.25) = -3.9375 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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