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Simplifying x2 + x = 183 Reorder the terms: x + x2 = 183 Solving x + x2 = 183 Solving for variable 'x'. Reorder the terms: -183 + x + x2 = 183 + -183 Combine like terms: 183 + -183 = 0 -183 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '183' to each side of the equation. -183 + x + 183 + x2 = 0 + 183 Reorder the terms: -183 + 183 + x + x2 = 0 + 183 Combine like terms: -183 + 183 = 0 0 + x + x2 = 0 + 183 x + x2 = 0 + 183 Combine like terms: 0 + 183 = 183 x + x2 = 183 The x term is x. 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. x + 0.25 + x2 = 183 + 0.25 Reorder the terms: 0.25 + x + x2 = 183 + 0.25 Combine like terms: 183 + 0.25 = 183.25 0.25 + x + x2 = 183.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 183.25 Calculate the square root of the right side: 13.536986371 Break this problem into two subproblems by setting (x + 0.5) equal to 13.536986371 and -13.536986371.Subproblem 1
x + 0.5 = 13.536986371 Simplifying x + 0.5 = 13.536986371 Reorder the terms: 0.5 + x = 13.536986371 Solving 0.5 + x = 13.536986371 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 13.536986371 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 13.536986371 + -0.5 x = 13.536986371 + -0.5 Combine like terms: 13.536986371 + -0.5 = 13.036986371 x = 13.036986371 Simplifying x = 13.036986371Subproblem 2
x + 0.5 = -13.536986371 Simplifying x + 0.5 = -13.536986371 Reorder the terms: 0.5 + x = -13.536986371 Solving 0.5 + x = -13.536986371 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -13.536986371 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -13.536986371 + -0.5 x = -13.536986371 + -0.5 Combine like terms: -13.536986371 + -0.5 = -14.036986371 x = -14.036986371 Simplifying x = -14.036986371Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.036986371, -14.036986371}
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