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Simplifying x2 + x + -166 = 0 Reorder the terms: -166 + x + x2 = 0 Solving -166 + x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '166' to each side of the equation. -166 + x + 166 + x2 = 0 + 166 Reorder the terms: -166 + 166 + x + x2 = 0 + 166 Combine like terms: -166 + 166 = 0 0 + x + x2 = 0 + 166 x + x2 = 0 + 166 Combine like terms: 0 + 166 = 166 x + x2 = 166 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 = 166 + 0.25 Reorder the terms: 0.25 + x + x2 = 166 + 0.25 Combine like terms: 166 + 0.25 = 166.25 0.25 + x + x2 = 166.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 166.25 Calculate the square root of the right side: 12.893796958 Break this problem into two subproblems by setting (x + 0.5) equal to 12.893796958 and -12.893796958.Subproblem 1
x + 0.5 = 12.893796958 Simplifying x + 0.5 = 12.893796958 Reorder the terms: 0.5 + x = 12.893796958 Solving 0.5 + x = 12.893796958 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 = 12.893796958 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 12.893796958 + -0.5 x = 12.893796958 + -0.5 Combine like terms: 12.893796958 + -0.5 = 12.393796958 x = 12.393796958 Simplifying x = 12.393796958Subproblem 2
x + 0.5 = -12.893796958 Simplifying x + 0.5 = -12.893796958 Reorder the terms: 0.5 + x = -12.893796958 Solving 0.5 + x = -12.893796958 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 = -12.893796958 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -12.893796958 + -0.5 x = -12.893796958 + -0.5 Combine like terms: -12.893796958 + -0.5 = -13.393796958 x = -13.393796958 Simplifying x = -13.393796958Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.393796958, -13.393796958}
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