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Simplifying z2 + z = 144 Reorder the terms: z + z2 = 144 Solving z + z2 = 144 Solving for variable 'z'. Reorder the terms: -144 + z + z2 = 144 + -144 Combine like terms: 144 + -144 = 0 -144 + z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '144' to each side of the equation. -144 + z + 144 + z2 = 0 + 144 Reorder the terms: -144 + 144 + z + z2 = 0 + 144 Combine like terms: -144 + 144 = 0 0 + z + z2 = 0 + 144 z + z2 = 0 + 144 Combine like terms: 0 + 144 = 144 z + z2 = 144 The z term is z. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. z + 0.25 + z2 = 144 + 0.25 Reorder the terms: 0.25 + z + z2 = 144 + 0.25 Combine like terms: 144 + 0.25 = 144.25 0.25 + z + z2 = 144.25 Factor a perfect square on the left side: (z + 0.5)(z + 0.5) = 144.25 Calculate the square root of the right side: 12.010412149 Break this problem into two subproblems by setting (z + 0.5) equal to 12.010412149 and -12.010412149.Subproblem 1
z + 0.5 = 12.010412149 Simplifying z + 0.5 = 12.010412149 Reorder the terms: 0.5 + z = 12.010412149 Solving 0.5 + z = 12.010412149 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + z = 12.010412149 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + z = 12.010412149 + -0.5 z = 12.010412149 + -0.5 Combine like terms: 12.010412149 + -0.5 = 11.510412149 z = 11.510412149 Simplifying z = 11.510412149Subproblem 2
z + 0.5 = -12.010412149 Simplifying z + 0.5 = -12.010412149 Reorder the terms: 0.5 + z = -12.010412149 Solving 0.5 + z = -12.010412149 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + z = -12.010412149 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + z = -12.010412149 + -0.5 z = -12.010412149 + -0.5 Combine like terms: -12.010412149 + -0.5 = -12.510412149 z = -12.510412149 Simplifying z = -12.510412149Solution
The solution to the problem is based on the solutions from the subproblems. z = {11.510412149, -12.510412149}
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