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Simplifying 2z2 = 30 + 7z Solving 2z2 = 30 + 7z Solving for variable 'z'. Reorder the terms: -30 + -7z + 2z2 = 30 + 7z + -30 + -7z Reorder the terms: -30 + -7z + 2z2 = 30 + -30 + 7z + -7z Combine like terms: 30 + -30 = 0 -30 + -7z + 2z2 = 0 + 7z + -7z -30 + -7z + 2z2 = 7z + -7z Combine like terms: 7z + -7z = 0 -30 + -7z + 2z2 = 0 Factor a trinomial. (-5 + -2z)(6 + -1z) = 0Subproblem 1
Set the factor '(-5 + -2z)' equal to zero and attempt to solve: Simplifying -5 + -2z = 0 Solving -5 + -2z = 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 + -2z = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2z = 0 + 5 -2z = 0 + 5 Combine like terms: 0 + 5 = 5 -2z = 5 Divide each side by '-2'. z = -2.5 Simplifying z = -2.5Subproblem 2
Set the factor '(6 + -1z)' equal to zero and attempt to solve: Simplifying 6 + -1z = 0 Solving 6 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1z = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1z = 0 + -6 -1z = 0 + -6 Combine like terms: 0 + -6 = -6 -1z = -6 Divide each side by '-1'. z = 6 Simplifying z = 6Solution
z = {-2.5, 6}
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