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Simplifying z2 + -12z = -9 Reorder the terms: -12z + z2 = -9 Solving -12z + z2 = -9 Solving for variable 'z'. Reorder the terms: 9 + -12z + z2 = -9 + 9 Combine like terms: -9 + 9 = 0 9 + -12z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + -12z + -9 + z2 = 0 + -9 Reorder the terms: 9 + -9 + -12z + z2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -12z + z2 = 0 + -9 -12z + z2 = 0 + -9 Combine like terms: 0 + -9 = -9 -12z + z2 = -9 The z term is -12z. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12z + 36 + z2 = -9 + 36 Reorder the terms: 36 + -12z + z2 = -9 + 36 Combine like terms: -9 + 36 = 27 36 + -12z + z2 = 27 Factor a perfect square on the left side: (z + -6)(z + -6) = 27 Calculate the square root of the right side: 5.196152423 Break this problem into two subproblems by setting (z + -6) equal to 5.196152423 and -5.196152423.Subproblem 1
z + -6 = 5.196152423 Simplifying z + -6 = 5.196152423 Reorder the terms: -6 + z = 5.196152423 Solving -6 + z = 5.196152423 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + z = 5.196152423 + 6 Combine like terms: -6 + 6 = 0 0 + z = 5.196152423 + 6 z = 5.196152423 + 6 Combine like terms: 5.196152423 + 6 = 11.196152423 z = 11.196152423 Simplifying z = 11.196152423Subproblem 2
z + -6 = -5.196152423 Simplifying z + -6 = -5.196152423 Reorder the terms: -6 + z = -5.196152423 Solving -6 + z = -5.196152423 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + z = -5.196152423 + 6 Combine like terms: -6 + 6 = 0 0 + z = -5.196152423 + 6 z = -5.196152423 + 6 Combine like terms: -5.196152423 + 6 = 0.803847577 z = 0.803847577 Simplifying z = 0.803847577Solution
The solution to the problem is based on the solutions from the subproblems. z = {11.196152423, 0.803847577}
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