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Simplifying x2 + 181x = 11 Reorder the terms: 181x + x2 = 11 Solving 181x + x2 = 11 Solving for variable 'x'. Reorder the terms: -11 + 181x + x2 = 11 + -11 Combine like terms: 11 + -11 = 0 -11 + 181x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + 181x + 11 + x2 = 0 + 11 Reorder the terms: -11 + 11 + 181x + x2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 181x + x2 = 0 + 11 181x + x2 = 0 + 11 Combine like terms: 0 + 11 = 11 181x + x2 = 11 The x term is 181x. Take half its coefficient (90.5). Square it (8190.25) and add it to both sides. Add '8190.25' to each side of the equation. 181x + 8190.25 + x2 = 11 + 8190.25 Reorder the terms: 8190.25 + 181x + x2 = 11 + 8190.25 Combine like terms: 11 + 8190.25 = 8201.25 8190.25 + 181x + x2 = 8201.25 Factor a perfect square on the left side: (x + 90.5)(x + 90.5) = 8201.25 Calculate the square root of the right side: 90.560753089 Break this problem into two subproblems by setting (x + 90.5) equal to 90.560753089 and -90.560753089.Subproblem 1
x + 90.5 = 90.560753089 Simplifying x + 90.5 = 90.560753089 Reorder the terms: 90.5 + x = 90.560753089 Solving 90.5 + x = 90.560753089 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-90.5' to each side of the equation. 90.5 + -90.5 + x = 90.560753089 + -90.5 Combine like terms: 90.5 + -90.5 = 0.0 0.0 + x = 90.560753089 + -90.5 x = 90.560753089 + -90.5 Combine like terms: 90.560753089 + -90.5 = 0.060753089 x = 0.060753089 Simplifying x = 0.060753089Subproblem 2
x + 90.5 = -90.560753089 Simplifying x + 90.5 = -90.560753089 Reorder the terms: 90.5 + x = -90.560753089 Solving 90.5 + x = -90.560753089 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-90.5' to each side of the equation. 90.5 + -90.5 + x = -90.560753089 + -90.5 Combine like terms: 90.5 + -90.5 = 0.0 0.0 + x = -90.560753089 + -90.5 x = -90.560753089 + -90.5 Combine like terms: -90.560753089 + -90.5 = -181.060753089 x = -181.060753089 Simplifying x = -181.060753089Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.060753089, -181.060753089}
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