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Simplifying 6a2 + 18a + 24 = 0 Reorder the terms: 24 + 18a + 6a2 = 0 Solving 24 + 18a + 6a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '6'. 6(4 + 3a + a2) = 0 Ignore the factor 6.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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