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Simplifying 8z2 = 18 + -70z Solving 8z2 = 18 + -70z Solving for variable 'z'. Reorder the terms: -18 + 70z + 8z2 = 18 + -70z + -18 + 70z Reorder the terms: -18 + 70z + 8z2 = 18 + -18 + -70z + 70z Combine like terms: 18 + -18 = 0 -18 + 70z + 8z2 = 0 + -70z + 70z -18 + 70z + 8z2 = -70z + 70z Combine like terms: -70z + 70z = 0 -18 + 70z + 8z2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-9 + 35z + 4z2) = 0 Factor a trinomial. 2((-9 + -1z)(1 + -4z)) = 0 Ignore the factor 2.Subproblem 1
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 = -9Subproblem 2
Set the factor '(1 + -4z)' equal to zero and attempt to solve: Simplifying 1 + -4z = 0 Solving 1 + -4z = 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 + -4z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4z = 0 + -1 -4z = 0 + -1 Combine like terms: 0 + -1 = -1 -4z = -1 Divide each side by '-4'. z = 0.25 Simplifying z = 0.25Solution
z = {-9, 0.25}
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