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Simplifying 16z2 + -54z + 35 = 0 Reorder the terms: 35 + -54z + 16z2 = 0 Solving 35 + -54z + 16z2 = 0 Solving for variable 'z'. Factor a trinomial. (7 + -8z)(5 + -2z) = 0Subproblem 1
Set the factor '(7 + -8z)' equal to zero and attempt to solve: Simplifying 7 + -8z = 0 Solving 7 + -8z = 0 Move all terms containing z to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -8z = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -8z = 0 + -7 -8z = 0 + -7 Combine like terms: 0 + -7 = -7 -8z = -7 Divide each side by '-8'. z = 0.875 Simplifying z = 0.875Subproblem 2
Set the factor '(5 + -2z)' equal to zero and attempt to solve: Simplifying 5 + -2z = 0 Solving 5 + -2z = 0 Move all terms containing z to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -2z = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2z = 0 + -5 -2z = 0 + -5 Combine like terms: 0 + -5 = -5 -2z = -5 Divide each side by '-2'. z = 2.5 Simplifying z = 2.5Solution
z = {0.875, 2.5}
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