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Simplifying z3 + -6z2 + 10z = 0 Reorder the terms: 10z + -6z2 + z3 = 0 Solving 10z + -6z2 + z3 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), 'z'. z(10 + -6z + 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 '(10 + -6z + z2)' equal to zero and attempt to solve: Simplifying 10 + -6z + z2 = 0 Solving 10 + -6z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '-10' to each side of the equation. 10 + -6z + -10 + z2 = 0 + -10 Reorder the terms: 10 + -10 + -6z + z2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -6z + z2 = 0 + -10 -6z + z2 = 0 + -10 Combine like terms: 0 + -10 = -10 -6z + z2 = -10 The z term is -6z. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6z + 9 + z2 = -10 + 9 Reorder the terms: 9 + -6z + z2 = -10 + 9 Combine like terms: -10 + 9 = -1 9 + -6z + z2 = -1 Factor a perfect square on the left side: (z + -3)(z + -3) = -1 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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