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Simplifying 2a2 + 12a = -40 Reorder the terms: 12a + 2a2 = -40 Solving 12a + 2a2 = -40 Solving for variable 'a'. Reorder the terms: 40 + 12a + 2a2 = -40 + 40 Combine like terms: -40 + 40 = 0 40 + 12a + 2a2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(20 + 6a + a2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(20 + 6a + a2)' equal to zero and attempt to solve: Simplifying 20 + 6a + a2 = 0 Solving 20 + 6a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '-20' to each side of the equation. 20 + 6a + -20 + a2 = 0 + -20 Reorder the terms: 20 + -20 + 6a + a2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + 6a + a2 = 0 + -20 6a + a2 = 0 + -20 Combine like terms: 0 + -20 = -20 6a + a2 = -20 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 = -20 + 9 Reorder the terms: 9 + 6a + a2 = -20 + 9 Combine like terms: -20 + 9 = -11 9 + 6a + a2 = -11 Factor a perfect square on the left side: (a + 3)(a + 3) = -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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