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Simplifying z2 + -8z = 64 Reorder the terms: -8z + z2 = 64 Solving -8z + z2 = 64 Solving for variable 'z'. Reorder the terms: -64 + -8z + z2 = 64 + -64 Combine like terms: 64 + -64 = 0 -64 + -8z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '64' to each side of the equation. -64 + -8z + 64 + z2 = 0 + 64 Reorder the terms: -64 + 64 + -8z + z2 = 0 + 64 Combine like terms: -64 + 64 = 0 0 + -8z + z2 = 0 + 64 -8z + z2 = 0 + 64 Combine like terms: 0 + 64 = 64 -8z + z2 = 64 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 = 64 + 16 Reorder the terms: 16 + -8z + z2 = 64 + 16 Combine like terms: 64 + 16 = 80 16 + -8z + z2 = 80 Factor a perfect square on the left side: (z + -4)(z + -4) = 80 Calculate the square root of the right side: 8.94427191 Break this problem into two subproblems by setting (z + -4) equal to 8.94427191 and -8.94427191.Subproblem 1
z + -4 = 8.94427191 Simplifying z + -4 = 8.94427191 Reorder the terms: -4 + z = 8.94427191 Solving -4 + z = 8.94427191 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 = 8.94427191 + 4 Combine like terms: -4 + 4 = 0 0 + z = 8.94427191 + 4 z = 8.94427191 + 4 Combine like terms: 8.94427191 + 4 = 12.94427191 z = 12.94427191 Simplifying z = 12.94427191Subproblem 2
z + -4 = -8.94427191 Simplifying z + -4 = -8.94427191 Reorder the terms: -4 + z = -8.94427191 Solving -4 + z = -8.94427191 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 = -8.94427191 + 4 Combine like terms: -4 + 4 = 0 0 + z = -8.94427191 + 4 z = -8.94427191 + 4 Combine like terms: -8.94427191 + 4 = -4.94427191 z = -4.94427191 Simplifying z = -4.94427191Solution
The solution to the problem is based on the solutions from the subproblems. z = {12.94427191, -4.94427191}
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