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Simplifying 5z2 + -22z + 8 = 0 Reorder the terms: 8 + -22z + 5z2 = 0 Solving 8 + -22z + 5z2 = 0 Solving for variable 'z'. Factor a trinomial. (2 + -5z)(4 + -1z) = 0Subproblem 1
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 = 0.4Subproblem 2
Set the factor '(4 + -1z)' equal to zero and attempt to solve: Simplifying 4 + -1z = 0 Solving 4 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1z = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1z = 0 + -4 -1z = 0 + -4 Combine like terms: 0 + -4 = -4 -1z = -4 Divide each side by '-1'. z = 4 Simplifying z = 4Solution
z = {0.4, 4}
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