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Simplifying 4z2 + 16z = 65 Reorder the terms: 16z + 4z2 = 65 Solving 16z + 4z2 = 65 Solving for variable 'z'. Reorder the terms: -65 + 16z + 4z2 = 65 + -65 Combine like terms: 65 + -65 = 0 -65 + 16z + 4z2 = 0 Factor a trinomial. (-13 + -2z)(5 + -2z) = 0Subproblem 1
Set the factor '(-13 + -2z)' equal to zero and attempt to solve: Simplifying -13 + -2z = 0 Solving -13 + -2z = 0 Move all terms containing z to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + -2z = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -2z = 0 + 13 -2z = 0 + 13 Combine like terms: 0 + 13 = 13 -2z = 13 Divide each side by '-2'. z = -6.5 Simplifying z = -6.5Subproblem 2
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 = 2.5Solution
z = {-6.5, 2.5}
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