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Simplifying 3 + 2a + a2 + 5 + -8a + a2 = 0 Reorder the terms: 3 + 5 + 2a + -8a + a2 + a2 = 0 Combine like terms: 3 + 5 = 8 8 + 2a + -8a + a2 + a2 = 0 Combine like terms: 2a + -8a = -6a 8 + -6a + a2 + a2 = 0 Combine like terms: a2 + a2 = 2a2 8 + -6a + 2a2 = 0 Solving 8 + -6a + 2a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2'. 2(4 + -3a + a2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4 + -3a + a2)' equal to zero and attempt to solve: Simplifying 4 + -3a + a2 = 0 Solving 4 + -3a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + -3a + -4 + a2 = 0 + -4 Reorder the terms: 4 + -4 + -3a + a2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3a + a2 = 0 + -4 -3a + a2 = 0 + -4 Combine like terms: 0 + -4 = -4 -3a + a2 = -4 The a term is -3a. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3a + 2.25 + a2 = -4 + 2.25 Reorder the terms: 2.25 + -3a + a2 = -4 + 2.25 Combine like terms: -4 + 2.25 = -1.75 2.25 + -3a + a2 = -1.75 Factor a perfect square on the left side: (a + -1.5)(a + -1.5) = -1.75 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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