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Simplifying 18z2 + 84z + 98 = 0 Reorder the terms: 98 + 84z + 18z2 = 0 Solving 98 + 84z + 18z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '2'. 2(49 + 42z + 9z2) = 0 Factor a trinomial. 2((7 + 3z)(7 + 3z)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7 + 3z)' equal to zero and attempt to solve: Simplifying 7 + 3z = 0 Solving 7 + 3z = 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 + 3z = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 3z = 0 + -7 3z = 0 + -7 Combine like terms: 0 + -7 = -7 3z = -7 Divide each side by '3'. z = -2.333333333 Simplifying z = -2.333333333Subproblem 2
Set the factor '(7 + 3z)' equal to zero and attempt to solve: Simplifying 7 + 3z = 0 Solving 7 + 3z = 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 + 3z = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 3z = 0 + -7 3z = 0 + -7 Combine like terms: 0 + -7 = -7 3z = -7 Divide each side by '3'. z = -2.333333333 Simplifying z = -2.333333333Solution
z = {-2.333333333, -2.333333333}
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