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Simplifying z2 + -5z + -2 = 34 Reorder the terms: -2 + -5z + z2 = 34 Solving -2 + -5z + z2 = 34 Solving for variable 'z'. Reorder the terms: -2 + -34 + -5z + z2 = 34 + -34 Combine like terms: -2 + -34 = -36 -36 + -5z + z2 = 34 + -34 Combine like terms: 34 + -34 = 0 -36 + -5z + z2 = 0 Factor a trinomial. (-4 + -1z)(9 + -1z) = 0Subproblem 1
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 = -4Subproblem 2
Set the factor '(9 + -1z)' equal to zero and attempt to solve: Simplifying 9 + -1z = 0 Solving 9 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1z = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1z = 0 + -9 -1z = 0 + -9 Combine like terms: 0 + -9 = -9 -1z = -9 Divide each side by '-1'. z = 9 Simplifying z = 9Solution
z = {-4, 9}
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