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Simplifying (9z + 11)(z + 9) = 79 Reorder the terms: (11 + 9z)(z + 9) = 79 Reorder the terms: (11 + 9z)(9 + z) = 79 Multiply (11 + 9z) * (9 + z) (11(9 + z) + 9z * (9 + z)) = 79 ((9 * 11 + z * 11) + 9z * (9 + z)) = 79 ((99 + 11z) + 9z * (9 + z)) = 79 (99 + 11z + (9 * 9z + z * 9z)) = 79 (99 + 11z + (81z + 9z2)) = 79 Combine like terms: 11z + 81z = 92z (99 + 92z + 9z2) = 79 Solving 99 + 92z + 9z2 = 79 Solving for variable 'z'. Reorder the terms: 99 + -79 + 92z + 9z2 = 79 + -79 Combine like terms: 99 + -79 = 20 20 + 92z + 9z2 = 79 + -79 Combine like terms: 79 + -79 = 0 20 + 92z + 9z2 = 0 Factor a trinomial. (10 + z)(2 + 9z) = 0Subproblem 1
Set the factor '(10 + z)' equal to zero and attempt to solve: Simplifying 10 + z = 0 Solving 10 + z = 0 Move all terms containing z to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + z = 0 + -10 Combine like terms: 10 + -10 = 0 0 + z = 0 + -10 z = 0 + -10 Combine like terms: 0 + -10 = -10 z = -10 Simplifying z = -10Subproblem 2
Set the factor '(2 + 9z)' equal to zero and attempt to solve: Simplifying 2 + 9z = 0 Solving 2 + 9z = 0 Move all terms containing z to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 9z = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 9z = 0 + -2 9z = 0 + -2 Combine like terms: 0 + -2 = -2 9z = -2 Divide each side by '9'. z = -0.2222222222 Simplifying z = -0.2222222222Solution
z = {-10, -0.2222222222}
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