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Simplifying 2a2 + 16a = -54 Reorder the terms: 16a + 2a2 = -54 Solving 16a + 2a2 = -54 Solving for variable 'a'. Reorder the terms: 54 + 16a + 2a2 = -54 + 54 Combine like terms: -54 + 54 = 0 54 + 16a + 2a2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(27 + 8a + a2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(27 + 8a + a2)' equal to zero and attempt to solve: Simplifying 27 + 8a + a2 = 0 Solving 27 + 8a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '-27' to each side of the equation. 27 + 8a + -27 + a2 = 0 + -27 Reorder the terms: 27 + -27 + 8a + a2 = 0 + -27 Combine like terms: 27 + -27 = 0 0 + 8a + a2 = 0 + -27 8a + a2 = 0 + -27 Combine like terms: 0 + -27 = -27 8a + a2 = -27 The a term is 8a. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8a + 16 + a2 = -27 + 16 Reorder the terms: 16 + 8a + a2 = -27 + 16 Combine like terms: -27 + 16 = -11 16 + 8a + a2 = -11 Factor a perfect square on the left side: (a + 4)(a + 4) = -11 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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