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Simplifying 2a2 + 4a = -24 Reorder the terms: 4a + 2a2 = -24 Solving 4a + 2a2 = -24 Solving for variable 'a'. Reorder the terms: 24 + 4a + 2a2 = -24 + 24 Combine like terms: -24 + 24 = 0 24 + 4a + 2a2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(12 + 2a + a2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(12 + 2a + a2)' equal to zero and attempt to solve: Simplifying 12 + 2a + a2 = 0 Solving 12 + 2a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '-12' to each side of the equation. 12 + 2a + -12 + a2 = 0 + -12 Reorder the terms: 12 + -12 + 2a + a2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + 2a + a2 = 0 + -12 2a + a2 = 0 + -12 Combine like terms: 0 + -12 = -12 2a + a2 = -12 The a term is 2a. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2a + 1 + a2 = -12 + 1 Reorder the terms: 1 + 2a + a2 = -12 + 1 Combine like terms: -12 + 1 = -11 1 + 2a + a2 = -11 Factor a perfect square on the left side: (a + 1)(a + 1) = -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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