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Simplifying 2z3 + 6z2 + 18z = 0 Reorder the terms: 18z + 6z2 + 2z3 = 0 Solving 18z + 6z2 + 2z3 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '2z'. 2z(9 + 3z + z2) = 0 Ignore the factor 2.Subproblem 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 '(9 + 3z + z2)' equal to zero and attempt to solve: Simplifying 9 + 3z + z2 = 0 Solving 9 + 3z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + 3z + -9 + z2 = 0 + -9 Reorder the terms: 9 + -9 + 3z + z2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 3z + z2 = 0 + -9 3z + z2 = 0 + -9 Combine like terms: 0 + -9 = -9 3z + z2 = -9 The z term is 3z. 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. 3z + 2.25 + z2 = -9 + 2.25 Reorder the terms: 2.25 + 3z + z2 = -9 + 2.25 Combine like terms: -9 + 2.25 = -6.75 2.25 + 3z + z2 = -6.75 Factor a perfect square on the left side: (z + 1.5)(z + 1.5) = -6.75 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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