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Simplifying 45z2 = 24 + -13z Solving 45z2 = 24 + -13z Solving for variable 'z'. Reorder the terms: -24 + 13z + 45z2 = 24 + -13z + -24 + 13z Reorder the terms: -24 + 13z + 45z2 = 24 + -24 + -13z + 13z Combine like terms: 24 + -24 = 0 -24 + 13z + 45z2 = 0 + -13z + 13z -24 + 13z + 45z2 = -13z + 13z Combine like terms: -13z + 13z = 0 -24 + 13z + 45z2 = 0 Factor a trinomial. (-8 + -9z)(3 + -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 '(3 + -5z)' equal to zero and attempt to solve: Simplifying 3 + -5z = 0 Solving 3 + -5z = 0 Move all terms containing z to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -5z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5z = 0 + -3 -5z = 0 + -3 Combine like terms: 0 + -3 = -3 -5z = -3 Divide each side by '-5'. z = 0.6 Simplifying z = 0.6Solution
z = {-0.8888888889, 0.6}
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