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Simplifying 3a2 + 9a + 30 = 0 Reorder the terms: 30 + 9a + 3a2 = 0 Solving 30 + 9a + 3a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '3'. 3(10 + 3a + a2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(10 + 3a + a2)' equal to zero and attempt to solve: Simplifying 10 + 3a + a2 = 0 Solving 10 + 3a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '-10' to each side of the equation. 10 + 3a + -10 + a2 = 0 + -10 Reorder the terms: 10 + -10 + 3a + a2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + 3a + a2 = 0 + -10 3a + a2 = 0 + -10 Combine like terms: 0 + -10 = -10 3a + a2 = -10 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 = -10 + 2.25 Reorder the terms: 2.25 + 3a + a2 = -10 + 2.25 Combine like terms: -10 + 2.25 = -7.75 2.25 + 3a + a2 = -7.75 Factor a perfect square on the left side: (a + 1.5)(a + 1.5) = -7.75 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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