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Simplifying 3a2 + 27a + 1200 = 0 Reorder the terms: 1200 + 27a + 3a2 = 0 Solving 1200 + 27a + 3a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '3'. 3(400 + 9a + a2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(400 + 9a + a2)' equal to zero and attempt to solve: Simplifying 400 + 9a + a2 = 0 Solving 400 + 9a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '-400' to each side of the equation. 400 + 9a + -400 + a2 = 0 + -400 Reorder the terms: 400 + -400 + 9a + a2 = 0 + -400 Combine like terms: 400 + -400 = 0 0 + 9a + a2 = 0 + -400 9a + a2 = 0 + -400 Combine like terms: 0 + -400 = -400 9a + a2 = -400 The a term is 9a. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9a + 20.25 + a2 = -400 + 20.25 Reorder the terms: 20.25 + 9a + a2 = -400 + 20.25 Combine like terms: -400 + 20.25 = -379.75 20.25 + 9a + a2 = -379.75 Factor a perfect square on the left side: (a + 4.5)(a + 4.5) = -379.75 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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