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Simplifying -5a4z + -15a3z + -25a2z = 0 Reorder the terms: -25a2z + -15a3z + -5a4z = 0 Solving -25a2z + -15a3z + -5a4z = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '-5a2z'. -5a2z(5 + 3a + a2) = 0 Ignore the factor -5.Subproblem 1
Set the factor 'a2z' equal to zero and attempt to solve: Simplifying a2z = 0 Solving a2z = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a2z = 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 '(5 + 3a + a2)' equal to zero and attempt to solve: Simplifying 5 + 3a + a2 = 0 Solving 5 + 3a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + 3a + -5 + a2 = 0 + -5 Reorder the terms: 5 + -5 + 3a + a2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 3a + a2 = 0 + -5 3a + a2 = 0 + -5 Combine like terms: 0 + -5 = -5 3a + a2 = -5 The a term is 3a. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3a + 2.25 + a2 = -5 + 2.25 Reorder the terms: 2.25 + 3a + a2 = -5 + 2.25 Combine like terms: -5 + 2.25 = -2.75 2.25 + 3a + a2 = -2.75 Factor a perfect square on the left side: (a + 1.5)(a + 1.5) = -2.75 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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