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Simplifying 4z2 + 62z + -32 = 0 Reorder the terms: -32 + 62z + 4z2 = 0 Solving -32 + 62z + 4z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '2'. 2(-16 + 31z + 2z2) = 0 Factor a trinomial. 2((-16 + -1z)(1 + -2z)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-16 + -1z)' equal to zero and attempt to solve: Simplifying -16 + -1z = 0 Solving -16 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + -1z = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -1z = 0 + 16 -1z = 0 + 16 Combine like terms: 0 + 16 = 16 -1z = 16 Divide each side by '-1'. z = -16 Simplifying z = -16Subproblem 2
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 = 0.5Solution
z = {-16, 0.5}
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