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Simplifying (2z + -11)(2z + -7) = 0 Reorder the terms: (-11 + 2z)(2z + -7) = 0 Reorder the terms: (-11 + 2z)(-7 + 2z) = 0 Multiply (-11 + 2z) * (-7 + 2z) (-11(-7 + 2z) + 2z * (-7 + 2z)) = 0 ((-7 * -11 + 2z * -11) + 2z * (-7 + 2z)) = 0 ((77 + -22z) + 2z * (-7 + 2z)) = 0 (77 + -22z + (-7 * 2z + 2z * 2z)) = 0 (77 + -22z + (-14z + 4z2)) = 0 Combine like terms: -22z + -14z = -36z (77 + -36z + 4z2) = 0 Solving 77 + -36z + 4z2 = 0 Solving for variable 'z'. Factor a trinomial. (7 + -2z)(11 + -2z) = 0Subproblem 1
Set the factor '(7 + -2z)' equal to zero and attempt to solve: Simplifying 7 + -2z = 0 Solving 7 + -2z = 0 Move all terms containing z to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -2z = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2z = 0 + -7 -2z = 0 + -7 Combine like terms: 0 + -7 = -7 -2z = -7 Divide each side by '-2'. z = 3.5 Simplifying z = 3.5Subproblem 2
Set the factor '(11 + -2z)' equal to zero and attempt to solve: Simplifying 11 + -2z = 0 Solving 11 + -2z = 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 + -2z = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -2z = 0 + -11 -2z = 0 + -11 Combine like terms: 0 + -11 = -11 -2z = -11 Divide each side by '-2'. z = 5.5 Simplifying z = 5.5Solution
z = {3.5, 5.5}
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