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Simplifying z2 + 5z + 10z + 50 = 0 Reorder the terms: 50 + 5z + 10z + z2 = 0 Combine like terms: 5z + 10z = 15z 50 + 15z + z2 = 0 Solving 50 + 15z + z2 = 0 Solving for variable 'z'. Factor a trinomial. (10 + z)(5 + z) = 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 '(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 = {-10, -5}
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