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Simplifying 12z2 + -28z + 11 = 0 Reorder the terms: 11 + -28z + 12z2 = 0 Solving 11 + -28z + 12z2 = 0 Solving for variable 'z'. Factor a trinomial. (1 + -2z)(11 + -6z) = 0Subproblem 1
Set the factor '(1 + -2z)' equal to zero and attempt to solve: Simplifying 1 + -2z = 0 Solving 1 + -2z = 0 Move all terms containing z to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2z = 0 + -1 -2z = 0 + -1 Combine like terms: 0 + -1 = -1 -2z = -1 Divide each side by '-2'. z = 0.5 Simplifying z = 0.5Subproblem 2
Set the factor '(11 + -6z)' equal to zero and attempt to solve: Simplifying 11 + -6z = 0 Solving 11 + -6z = 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 + -6z = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -6z = 0 + -11 -6z = 0 + -11 Combine like terms: 0 + -11 = -11 -6z = -11 Divide each side by '-6'. z = 1.833333333 Simplifying z = 1.833333333Solution
z = {0.5, 1.833333333}
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