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Simplifying W(z) = 4z2 + -9z Multiply W * z zW = 4z2 + -9z Reorder the terms: zW = -9z + 4z2 Solving zW = -9z + 4z2 Solving for variable 'z'. Reorder the terms: 9z + zW + -4z2 = -9z + 4z2 + 9z + -4z2 Reorder the terms: 9z + zW + -4z2 = -9z + 9z + 4z2 + -4z2 Combine like terms: -9z + 9z = 0 9z + zW + -4z2 = 0 + 4z2 + -4z2 9z + zW + -4z2 = 4z2 + -4z2 Combine like terms: 4z2 + -4z2 = 0 9z + zW + -4z2 = 0 Factor out the Greatest Common Factor (GCF), 'z'. z(9 + W + -4z) = 0Subproblem 1
Set the factor 'z' equal to zero and attempt to solve: Simplifying z = 0 Solving z = 0 Move all terms containing z to the left, all other terms to the right. Simplifying z = 0Subproblem 2
Set the factor '(9 + W + -4z)' equal to zero and attempt to solve: Simplifying 9 + W + -4z = 0 Solving 9 + W + -4z = 0 Move all terms containing z to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + W + -9 + -4z = 0 + -9 Reorder the terms: 9 + -9 + W + -4z = 0 + -9 Combine like terms: 9 + -9 = 0 0 + W + -4z = 0 + -9 W + -4z = 0 + -9 Combine like terms: 0 + -9 = -9 W + -4z = -9 Add '-1W' to each side of the equation. W + -1W + -4z = -9 + -1W Combine like terms: W + -1W = 0 0 + -4z = -9 + -1W -4z = -9 + -1W Divide each side by '-4'. z = 2.25 + 0.25W Simplifying z = 2.25 + 0.25WSolution
z = {0, 2.25 + 0.25W}
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