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Simplifying 45z2 = 16 + -22z Solving 45z2 = 16 + -22z Solving for variable 'z'. Reorder the terms: -16 + 22z + 45z2 = 16 + -22z + -16 + 22z Reorder the terms: -16 + 22z + 45z2 = 16 + -16 + -22z + 22z Combine like terms: 16 + -16 = 0 -16 + 22z + 45z2 = 0 + -22z + 22z -16 + 22z + 45z2 = -22z + 22z Combine like terms: -22z + 22z = 0 -16 + 22z + 45z2 = 0 Factor a trinomial. (-8 + -9z)(2 + -5z) = 0Subproblem 1
Set the factor '(-8 + -9z)' equal to zero and attempt to solve: Simplifying -8 + -9z = 0 Solving -8 + -9z = 0 Move all terms containing z to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -9z = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -9z = 0 + 8 -9z = 0 + 8 Combine like terms: 0 + 8 = 8 -9z = 8 Divide each side by '-9'. z = -0.8888888889 Simplifying z = -0.8888888889Subproblem 2
Set the factor '(2 + -5z)' equal to zero and attempt to solve: Simplifying 2 + -5z = 0 Solving 2 + -5z = 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 + -5z = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5z = 0 + -2 -5z = 0 + -2 Combine like terms: 0 + -2 = -2 -5z = -2 Divide each side by '-5'. z = 0.4 Simplifying z = 0.4Solution
z = {-0.8888888889, 0.4}
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