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Simplifying (z + 8)(z + 8) = 9 Reorder the terms: (8 + z)(z + 8) = 9 Reorder the terms: (8 + z)(8 + z) = 9 Multiply (8 + z) * (8 + z) (8(8 + z) + z(8 + z)) = 9 ((8 * 8 + z * 8) + z(8 + z)) = 9 ((64 + 8z) + z(8 + z)) = 9 (64 + 8z + (8 * z + z * z)) = 9 (64 + 8z + (8z + z2)) = 9 Combine like terms: 8z + 8z = 16z (64 + 16z + z2) = 9 Solving 64 + 16z + z2 = 9 Solving for variable 'z'. Reorder the terms: 64 + -9 + 16z + z2 = 9 + -9 Combine like terms: 64 + -9 = 55 55 + 16z + z2 = 9 + -9 Combine like terms: 9 + -9 = 0 55 + 16z + z2 = 0 Factor a trinomial. (11 + z)(5 + z) = 0Subproblem 1
Set the factor '(11 + z)' equal to zero and attempt to solve: Simplifying 11 + z = 0 Solving 11 + z = 0 Move all terms containing z to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + z = 0 + -11 Combine like terms: 11 + -11 = 0 0 + z = 0 + -11 z = 0 + -11 Combine like terms: 0 + -11 = -11 z = -11 Simplifying z = -11Subproblem 2
Set the factor '(5 + z)' equal to zero and attempt to solve: Simplifying 5 + z = 0 Solving 5 + z = 0 Move all terms containing z to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + z = 0 + -5 Combine like terms: 5 + -5 = 0 0 + z = 0 + -5 z = 0 + -5 Combine like terms: 0 + -5 = -5 z = -5 Simplifying z = -5Solution
z = {-11, -5}
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