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Simplifying -2a2 + -3a + -63 = 0 Reorder the terms: -63 + -3a + -2a2 = 0 Solving -63 + -3a + -2a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '-1'. -1(63 + 3a + 2a2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(63 + 3a + 2a2)' equal to zero and attempt to solve: Simplifying 63 + 3a + 2a2 = 0 Solving 63 + 3a + 2a2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 31.5 + 1.5a + a2 = 0 Move the constant term to the right: Add '-31.5' to each side of the equation. 31.5 + 1.5a + -31.5 + a2 = 0 + -31.5 Reorder the terms: 31.5 + -31.5 + 1.5a + a2 = 0 + -31.5 Combine like terms: 31.5 + -31.5 = 0.0 0.0 + 1.5a + a2 = 0 + -31.5 1.5a + a2 = 0 + -31.5 Combine like terms: 0 + -31.5 = -31.5 1.5a + a2 = -31.5 The a term is 1.5a. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5a + 0.5625 + a2 = -31.5 + 0.5625 Reorder the terms: 0.5625 + 1.5a + a2 = -31.5 + 0.5625 Combine like terms: -31.5 + 0.5625 = -30.9375 0.5625 + 1.5a + a2 = -30.9375 Factor a perfect square on the left side: (a + 0.75)(a + 0.75) = -30.9375 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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