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Simplifying 15z2 = 5 + 22z Solving 15z2 = 5 + 22z Solving for variable 'z'. Reorder the terms: -5 + -22z + 15z2 = 5 + 22z + -5 + -22z Reorder the terms: -5 + -22z + 15z2 = 5 + -5 + 22z + -22z Combine like terms: 5 + -5 = 0 -5 + -22z + 15z2 = 0 + 22z + -22z -5 + -22z + 15z2 = 22z + -22z Combine like terms: 22z + -22z = 0 -5 + -22z + 15z2 = 0 Factor a trinomial. (-1 + -5z)(5 + -3z) = 0Subproblem 1
Set the factor '(-1 + -5z)' equal to zero and attempt to solve: Simplifying -1 + -5z = 0 Solving -1 + -5z = 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 + -5z = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -5z = 0 + 1 -5z = 0 + 1 Combine like terms: 0 + 1 = 1 -5z = 1 Divide each side by '-5'. z = -0.2 Simplifying z = -0.2Subproblem 2
Set the factor '(5 + -3z)' equal to zero and attempt to solve: Simplifying 5 + -3z = 0 Solving 5 + -3z = 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 + -3z = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3z = 0 + -5 -3z = 0 + -5 Combine like terms: 0 + -5 = -5 -3z = -5 Divide each side by '-3'. z = 1.666666667 Simplifying z = 1.666666667Solution
z = {-0.2, 1.666666667}
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