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Simplifying z(z + -5) = 2 Reorder the terms: z(-5 + z) = 2 (-5 * z + z * z) = 2 (-5z + z2) = 2 Solving -5z + z2 = 2 Solving for variable 'z'. Reorder the terms: -2 + -5z + z2 = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + -5z + z2 = 0 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 = 5.372281323 z = 5.372281323 Simplifying z = 5.372281323Subproblem 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 = -0.372281323 z = -0.372281323 Simplifying z = -0.372281323Solution
The solution to the problem is based on the solutions from the subproblems. z = {5.372281323, -0.372281323}
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