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Simplifying 18z2 + 54z + -44 = 0 Reorder the terms: -44 + 54z + 18z2 = 0 Solving -44 + 54z + 18z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '2'. 2(-22 + 27z + 9z2) = 0 Factor a trinomial. 2((-11 + -3z)(2 + -3z)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-11 + -3z)' equal to zero and attempt to solve: Simplifying -11 + -3z = 0 Solving -11 + -3z = 0 Move all terms containing z to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + -3z = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -3z = 0 + 11 -3z = 0 + 11 Combine like terms: 0 + 11 = 11 -3z = 11 Divide each side by '-3'. z = -3.666666667 Simplifying z = -3.666666667Subproblem 2
Set the factor '(2 + -3z)' equal to zero and attempt to solve: Simplifying 2 + -3z = 0 Solving 2 + -3z = 0 Move all terms containing z to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3z = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3z = 0 + -2 -3z = 0 + -2 Combine like terms: 0 + -2 = -2 -3z = -2 Divide each side by '-3'. z = 0.6666666667 Simplifying z = 0.6666666667Solution
z = {-3.666666667, 0.6666666667}
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