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Simplifying 2a2 + 2a + 24 = 0 Reorder the terms: 24 + 2a + 2a2 = 0 Solving 24 + 2a + 2a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2'. 2(12 + a + a2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(12 + a + a2)' equal to zero and attempt to solve: Simplifying 12 + a + a2 = 0 Solving 12 + a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '-12' to each side of the equation. 12 + a + -12 + a2 = 0 + -12 Reorder the terms: 12 + -12 + a + a2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + a + a2 = 0 + -12 a + a2 = 0 + -12 Combine like terms: 0 + -12 = -12 a + a2 = -12 The a term is a. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. a + 0.25 + a2 = -12 + 0.25 Reorder the terms: 0.25 + a + a2 = -12 + 0.25 Combine like terms: -12 + 0.25 = -11.75 0.25 + a + a2 = -11.75 Factor a perfect square on the left side: (a + 0.5)(a + 0.5) = -11.75 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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