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Simplifying z3 + z2 + 8z = 0 Reorder the terms: 8z + z2 + z3 = 0 Solving 8z + z2 + z3 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), 'z'. z(8 + z + z2) = 0Subproblem 1
Set the factor 'z' equal to zero and attempt to solve: Simplifying z = 0 Solving z = 0 Move all terms containing z to the left, all other terms to the right. Simplifying z = 0Subproblem 2
Set the factor '(8 + z + z2)' equal to zero and attempt to solve: Simplifying 8 + z + z2 = 0 Solving 8 + z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + z + -8 + z2 = 0 + -8 Reorder the terms: 8 + -8 + z + z2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + z + z2 = 0 + -8 z + z2 = 0 + -8 Combine like terms: 0 + -8 = -8 z + z2 = -8 The z term is z. 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. z + 0.25 + z2 = -8 + 0.25 Reorder the terms: 0.25 + z + z2 = -8 + 0.25 Combine like terms: -8 + 0.25 = -7.75 0.25 + z + z2 = -7.75 Factor a perfect square on the left side: (z + 0.5)(z + 0.5) = -7.75 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.Solution
z = {0}
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