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Simplifying (z2) + 11z + -468 = 0 z2 + 11z + -468 = 0 Reorder the terms: -468 + 11z + z2 = 0 Solving -468 + 11z + z2 = 0 Solving for variable 'z'. Begin completing the square. Move the constant term to the right: Add '468' to each side of the equation. -468 + 11z + 468 + z2 = 0 + 468 Reorder the terms: -468 + 468 + 11z + z2 = 0 + 468 Combine like terms: -468 + 468 = 0 0 + 11z + z2 = 0 + 468 11z + z2 = 0 + 468 Combine like terms: 0 + 468 = 468 11z + z2 = 468 The z term is 11z. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11z + 30.25 + z2 = 468 + 30.25 Reorder the terms: 30.25 + 11z + z2 = 468 + 30.25 Combine like terms: 468 + 30.25 = 498.25 30.25 + 11z + z2 = 498.25 Factor a perfect square on the left side: (z + 5.5)(z + 5.5) = 498.25 Calculate the square root of the right side: 22.321514286 Break this problem into two subproblems by setting (z + 5.5) equal to 22.321514286 and -22.321514286.Subproblem 1
z + 5.5 = 22.321514286 Simplifying z + 5.5 = 22.321514286 Reorder the terms: 5.5 + z = 22.321514286 Solving 5.5 + z = 22.321514286 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + z = 22.321514286 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + z = 22.321514286 + -5.5 z = 22.321514286 + -5.5 Combine like terms: 22.321514286 + -5.5 = 16.821514286 z = 16.821514286 Simplifying z = 16.821514286Subproblem 2
z + 5.5 = -22.321514286 Simplifying z + 5.5 = -22.321514286 Reorder the terms: 5.5 + z = -22.321514286 Solving 5.5 + z = -22.321514286 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + z = -22.321514286 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + z = -22.321514286 + -5.5 z = -22.321514286 + -5.5 Combine like terms: -22.321514286 + -5.5 = -27.821514286 z = -27.821514286 Simplifying z = -27.821514286Solution
The solution to the problem is based on the solutions from the subproblems. z = {16.821514286, -27.821514286}
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