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Simplifying z2 + -2z + -17 = 7 Reorder the terms: -17 + -2z + z2 = 7 Solving -17 + -2z + z2 = 7 Solving for variable 'z'. Reorder the terms: -17 + -7 + -2z + z2 = 7 + -7 Combine like terms: -17 + -7 = -24 -24 + -2z + z2 = 7 + -7 Combine like terms: 7 + -7 = 0 -24 + -2z + z2 = 0 Factor a trinomial. (-4 + -1z)(6 + -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 '(6 + -1z)' equal to zero and attempt to solve: Simplifying 6 + -1z = 0 Solving 6 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1z = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1z = 0 + -6 -1z = 0 + -6 Combine like terms: 0 + -6 = -6 -1z = -6 Divide each side by '-1'. z = 6 Simplifying z = 6Solution
z = {-4, 6}
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