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Simplifying -2z2 + -20z + -50 = -512 Reorder the terms: -50 + -20z + -2z2 = -512 Solving -50 + -20z + -2z2 = -512 Solving for variable 'z'. Reorder the terms: -50 + 512 + -20z + -2z2 = -512 + 512 Combine like terms: -50 + 512 = 462 462 + -20z + -2z2 = -512 + 512 Combine like terms: -512 + 512 = 0 462 + -20z + -2z2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(231 + -10z + -1z2) = 0 Factor a trinomial. 2((11 + -1z)(21 + z)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(11 + -1z)' equal to zero and attempt to solve: Simplifying 11 + -1z = 0 Solving 11 + -1z = 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 + -1z = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -1z = 0 + -11 -1z = 0 + -11 Combine like terms: 0 + -11 = -11 -1z = -11 Divide each side by '-1'. z = 11 Simplifying z = 11Subproblem 2
Set the factor '(21 + z)' equal to zero and attempt to solve: Simplifying 21 + z = 0 Solving 21 + z = 0 Move all terms containing z to the left, all other terms to the right. Add '-21' to each side of the equation. 21 + -21 + z = 0 + -21 Combine like terms: 21 + -21 = 0 0 + z = 0 + -21 z = 0 + -21 Combine like terms: 0 + -21 = -21 z = -21 Simplifying z = -21Solution
z = {11, -21}
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