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Simplifying z2 + -8z = -9 Reorder the terms: -8z + z2 = -9 Solving -8z + z2 = -9 Solving for variable 'z'. Reorder the terms: 9 + -8z + z2 = -9 + 9 Combine like terms: -9 + 9 = 0 9 + -8z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + -8z + -9 + z2 = 0 + -9 Reorder the terms: 9 + -9 + -8z + z2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -8z + z2 = 0 + -9 -8z + z2 = 0 + -9 Combine like terms: 0 + -9 = -9 -8z + z2 = -9 The z term is -8z. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8z + 16 + z2 = -9 + 16 Reorder the terms: 16 + -8z + z2 = -9 + 16 Combine like terms: -9 + 16 = 7 16 + -8z + z2 = 7 Factor a perfect square on the left side: (z + -4)(z + -4) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (z + -4) equal to 2.645751311 and -2.645751311.Subproblem 1
z + -4 = 2.645751311 Simplifying z + -4 = 2.645751311 Reorder the terms: -4 + z = 2.645751311 Solving -4 + z = 2.645751311 Solving for variable 'z'. 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 = 2.645751311 + 4 Combine like terms: -4 + 4 = 0 0 + z = 2.645751311 + 4 z = 2.645751311 + 4 Combine like terms: 2.645751311 + 4 = 6.645751311 z = 6.645751311 Simplifying z = 6.645751311Subproblem 2
z + -4 = -2.645751311 Simplifying z + -4 = -2.645751311 Reorder the terms: -4 + z = -2.645751311 Solving -4 + z = -2.645751311 Solving for variable 'z'. 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 = -2.645751311 + 4 Combine like terms: -4 + 4 = 0 0 + z = -2.645751311 + 4 z = -2.645751311 + 4 Combine like terms: -2.645751311 + 4 = 1.354248689 z = 1.354248689 Simplifying z = 1.354248689Solution
The solution to the problem is based on the solutions from the subproblems. z = {6.645751311, 1.354248689}
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