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Simplifying z2 + -1005z + 60080 = 0 Reorder the terms: 60080 + -1005z + z2 = 0 Solving 60080 + -1005z + z2 = 0 Solving for variable 'z'. Begin completing the square. Move the constant term to the right: Add '-60080' to each side of the equation. 60080 + -1005z + -60080 + z2 = 0 + -60080 Reorder the terms: 60080 + -60080 + -1005z + z2 = 0 + -60080 Combine like terms: 60080 + -60080 = 0 0 + -1005z + z2 = 0 + -60080 -1005z + z2 = 0 + -60080 Combine like terms: 0 + -60080 = -60080 -1005z + z2 = -60080 The z term is -1005z. Take half its coefficient (-502.5). Square it (252506.25) and add it to both sides. Add '252506.25' to each side of the equation. -1005z + 252506.25 + z2 = -60080 + 252506.25 Reorder the terms: 252506.25 + -1005z + z2 = -60080 + 252506.25 Combine like terms: -60080 + 252506.25 = 192426.25 252506.25 + -1005z + z2 = 192426.25 Factor a perfect square on the left side: (z + -502.5)(z + -502.5) = 192426.25 Calculate the square root of the right side: 438.664165393 Break this problem into two subproblems by setting (z + -502.5) equal to 438.664165393 and -438.664165393.Subproblem 1
z + -502.5 = 438.664165393 Simplifying z + -502.5 = 438.664165393 Reorder the terms: -502.5 + z = 438.664165393 Solving -502.5 + z = 438.664165393 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '502.5' to each side of the equation. -502.5 + 502.5 + z = 438.664165393 + 502.5 Combine like terms: -502.5 + 502.5 = 0.0 0.0 + z = 438.664165393 + 502.5 z = 438.664165393 + 502.5 Combine like terms: 438.664165393 + 502.5 = 941.164165393 z = 941.164165393 Simplifying z = 941.164165393Subproblem 2
z + -502.5 = -438.664165393 Simplifying z + -502.5 = -438.664165393 Reorder the terms: -502.5 + z = -438.664165393 Solving -502.5 + z = -438.664165393 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '502.5' to each side of the equation. -502.5 + 502.5 + z = -438.664165393 + 502.5 Combine like terms: -502.5 + 502.5 = 0.0 0.0 + z = -438.664165393 + 502.5 z = -438.664165393 + 502.5 Combine like terms: -438.664165393 + 502.5 = 63.835834607 z = 63.835834607 Simplifying z = 63.835834607Solution
The solution to the problem is based on the solutions from the subproblems. z = {941.164165393, 63.835834607}
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