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Simplifying 20 = 8z2 + -36z + 36 Reorder the terms: 20 = 36 + -36z + 8z2 Solving 20 = 36 + -36z + 8z2 Solving for variable 'z'. Combine like terms: 20 + -36 = -16 -16 + 36z + -8z2 = 36 + -36z + 8z2 + -36 + 36z + -8z2 Reorder the terms: -16 + 36z + -8z2 = 36 + -36 + -36z + 36z + 8z2 + -8z2 Combine like terms: 36 + -36 = 0 -16 + 36z + -8z2 = 0 + -36z + 36z + 8z2 + -8z2 -16 + 36z + -8z2 = -36z + 36z + 8z2 + -8z2 Combine like terms: -36z + 36z = 0 -16 + 36z + -8z2 = 0 + 8z2 + -8z2 -16 + 36z + -8z2 = 8z2 + -8z2 Combine like terms: 8z2 + -8z2 = 0 -16 + 36z + -8z2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-4 + 9z + -2z2) = 0 Factor a trinomial. 4((-4 + z)(1 + -2z)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-4 + z)' equal to zero and attempt to solve: Simplifying -4 + z = 0 Solving -4 + z = 0 Move all terms containing z to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + z = 0 + 4 Combine like terms: -4 + 4 = 0 0 + z = 0 + 4 z = 0 + 4 Combine like terms: 0 + 4 = 4 z = 4 Simplifying z = 4Subproblem 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 = {4, 0.5}
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