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Simplifying 2a2 + 12a = -30 Reorder the terms: 12a + 2a2 = -30 Solving 12a + 2a2 = -30 Solving for variable 'a'. Reorder the terms: 30 + 12a + 2a2 = -30 + 30 Combine like terms: -30 + 30 = 0 30 + 12a + 2a2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(15 + 6a + a2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(15 + 6a + a2)' equal to zero and attempt to solve: Simplifying 15 + 6a + a2 = 0 Solving 15 + 6a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '-15' to each side of the equation. 15 + 6a + -15 + a2 = 0 + -15 Reorder the terms: 15 + -15 + 6a + a2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + 6a + a2 = 0 + -15 6a + a2 = 0 + -15 Combine like terms: 0 + -15 = -15 6a + a2 = -15 The a term is 6a. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6a + 9 + a2 = -15 + 9 Reorder the terms: 9 + 6a + a2 = -15 + 9 Combine like terms: -15 + 9 = -6 9 + 6a + a2 = -6 Factor a perfect square on the left side: (a + 3)(a + 3) = -6 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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