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Simplifying 2a2 + -6a + 2 = -14 Reorder the terms: 2 + -6a + 2a2 = -14 Solving 2 + -6a + 2a2 = -14 Solving for variable 'a'. Reorder the terms: 2 + 14 + -6a + 2a2 = -14 + 14 Combine like terms: 2 + 14 = 16 16 + -6a + 2a2 = -14 + 14 Combine like terms: -14 + 14 = 0 16 + -6a + 2a2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(8 + -3a + a2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(8 + -3a + a2)' equal to zero and attempt to solve: Simplifying 8 + -3a + a2 = 0 Solving 8 + -3a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + -3a + -8 + a2 = 0 + -8 Reorder the terms: 8 + -8 + -3a + a2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -3a + a2 = 0 + -8 -3a + a2 = 0 + -8 Combine like terms: 0 + -8 = -8 -3a + a2 = -8 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 = -8 + 2.25 Reorder the terms: 2.25 + -3a + a2 = -8 + 2.25 Combine like terms: -8 + 2.25 = -5.75 2.25 + -3a + a2 = -5.75 Factor a perfect square on the left side: (a + -1.5)(a + -1.5) = -5.75 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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