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Simplifying 2a6 + 2a5 + 2a4 = 0 Reorder the terms: 2a4 + 2a5 + 2a6 = 0 Solving 2a4 + 2a5 + 2a6 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2a4'. 2a4(1 + a + a2) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'a4' equal to zero and attempt to solve: Simplifying a4 = 0 Solving a4 = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a4 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(1 + a + a2)' equal to zero and attempt to solve: Simplifying 1 + a + a2 = 0 Solving 1 + a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + a + -1 + a2 = 0 + -1 Reorder the terms: 1 + -1 + a + a2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + a + a2 = 0 + -1 a + a2 = 0 + -1 Combine like terms: 0 + -1 = -1 a + a2 = -1 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 = -1 + 0.25 Reorder the terms: 0.25 + a + a2 = -1 + 0.25 Combine like terms: -1 + 0.25 = -0.75 0.25 + a + a2 = -0.75 Factor a perfect square on the left side: (a + 0.5)(a + 0.5) = -0.75 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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