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Simplifying 8z + -22 = 3(3z + 11) * z Reorder the terms: -22 + 8z = 3(3z + 11) * z Reorder the terms: -22 + 8z = 3(11 + 3z) * z Reorder the terms for easier multiplication: -22 + 8z = 3z(11 + 3z) -22 + 8z = (11 * 3z + 3z * 3z) -22 + 8z = (33z + 9z2) Solving -22 + 8z = 33z + 9z2 Solving for variable 'z'. Combine like terms: 8z + -33z = -25z -22 + -25z + -9z2 = 33z + 9z2 + -33z + -9z2 Reorder the terms: -22 + -25z + -9z2 = 33z + -33z + 9z2 + -9z2 Combine like terms: 33z + -33z = 0 -22 + -25z + -9z2 = 0 + 9z2 + -9z2 -22 + -25z + -9z2 = 9z2 + -9z2 Combine like terms: 9z2 + -9z2 = 0 -22 + -25z + -9z2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(22 + 25z + 9z2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(22 + 25z + 9z2)' equal to zero and attempt to solve: Simplifying 22 + 25z + 9z2 = 0 Solving 22 + 25z + 9z2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 2.444444444 + 2.777777778z + z2 = 0 Move the constant term to the right: Add '-2.444444444' to each side of the equation. 2.444444444 + 2.777777778z + -2.444444444 + z2 = 0 + -2.444444444 Reorder the terms: 2.444444444 + -2.444444444 + 2.777777778z + z2 = 0 + -2.444444444 Combine like terms: 2.444444444 + -2.444444444 = 0.000000000 0.000000000 + 2.777777778z + z2 = 0 + -2.444444444 2.777777778z + z2 = 0 + -2.444444444 Combine like terms: 0 + -2.444444444 = -2.444444444 2.777777778z + z2 = -2.444444444 The z term is 2.777777778z. Take half its coefficient (1.388888889). Square it (1.929012346) and add it to both sides. Add '1.929012346' to each side of the equation. 2.777777778z + 1.929012346 + z2 = -2.444444444 + 1.929012346 Reorder the terms: 1.929012346 + 2.777777778z + z2 = -2.444444444 + 1.929012346 Combine like terms: -2.444444444 + 1.929012346 = -0.515432098 1.929012346 + 2.777777778z + z2 = -0.515432098 Factor a perfect square on the left side: (z + 1.388888889)(z + 1.388888889) = -0.515432098 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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