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Simplifying z2 + 5z + -2 = 0 Reorder the terms: -2 + 5z + z2 = 0 Solving -2 + 5z + z2 = 0 Solving for variable 'z'. Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + 5z + 2 + z2 = 0 + 2 Reorder the terms: -2 + 2 + 5z + z2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 5z + z2 = 0 + 2 5z + z2 = 0 + 2 Combine like terms: 0 + 2 = 2 5z + z2 = 2 The z term is 5z. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5z + 6.25 + z2 = 2 + 6.25 Reorder the terms: 6.25 + 5z + z2 = 2 + 6.25 Combine like terms: 2 + 6.25 = 8.25 6.25 + 5z + z2 = 8.25 Factor a perfect square on the left side: (z + 2.5)(z + 2.5) = 8.25 Calculate the square root of the right side: 2.872281323 Break this problem into two subproblems by setting (z + 2.5) equal to 2.872281323 and -2.872281323.Subproblem 1
z + 2.5 = 2.872281323 Simplifying z + 2.5 = 2.872281323 Reorder the terms: 2.5 + z = 2.872281323 Solving 2.5 + z = 2.872281323 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + z = 2.872281323 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + z = 2.872281323 + -2.5 z = 2.872281323 + -2.5 Combine like terms: 2.872281323 + -2.5 = 0.372281323 z = 0.372281323 Simplifying z = 0.372281323Subproblem 2
z + 2.5 = -2.872281323 Simplifying z + 2.5 = -2.872281323 Reorder the terms: 2.5 + z = -2.872281323 Solving 2.5 + z = -2.872281323 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + z = -2.872281323 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + z = -2.872281323 + -2.5 z = -2.872281323 + -2.5 Combine like terms: -2.872281323 + -2.5 = -5.372281323 z = -5.372281323 Simplifying z = -5.372281323Solution
The solution to the problem is based on the solutions from the subproblems. z = {0.372281323, -5.372281323}
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