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Simplifying 8z2 + -68z = -32 Reorder the terms: -68z + 8z2 = -32 Solving -68z + 8z2 = -32 Solving for variable 'z'. Reorder the terms: 32 + -68z + 8z2 = -32 + 32 Combine like terms: -32 + 32 = 0 32 + -68z + 8z2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(8 + -17z + 2z2) = 0 Factor a trinomial. 4((1 + -2z)(8 + -1z)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(1 + -2z)' equal to zero and attempt to solve: Simplifying 1 + -2z = 0 Solving 1 + -2z = 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 + -2z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2z = 0 + -1 -2z = 0 + -1 Combine like terms: 0 + -1 = -1 -2z = -1 Divide each side by '-2'. z = 0.5 Simplifying z = 0.5Subproblem 2
Set the factor '(8 + -1z)' equal to zero and attempt to solve: Simplifying 8 + -1z = 0 Solving 8 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1z = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1z = 0 + -8 -1z = 0 + -8 Combine like terms: 0 + -8 = -8 -1z = -8 Divide each side by '-1'. z = 8 Simplifying z = 8Solution
z = {0.5, 8}
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