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Simplifying -4a7 + 4a6 + -2a5 = 0 Reorder the terms: -2a5 + 4a6 + -4a7 = 0 Solving -2a5 + 4a6 + -4a7 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2a5'. 2a5(-1 + 2a + -2a2) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'a5' equal to zero and attempt to solve: Simplifying a5 = 0 Solving a5 = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a5 = 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 + 2a + -2a2)' equal to zero and attempt to solve: Simplifying -1 + 2a + -2a2 = 0 Solving -1 + 2a + -2a2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 0.5 + -1a + a2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -1a + -0.5 + a2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + -1a + a2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -1a + a2 = 0 + -0.5 -1a + a2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 -1a + a2 = -0.5 The a term is -1a. 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. -1a + 0.25 + a2 = -0.5 + 0.25 Reorder the terms: 0.25 + -1a + a2 = -0.5 + 0.25 Combine like terms: -0.5 + 0.25 = -0.25 0.25 + -1a + a2 = -0.25 Factor a perfect square on the left side: (a + -0.5)(a + -0.5) = -0.25 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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