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Simplifying x2 + -2x + -165 = 0 Reorder the terms: -165 + -2x + x2 = 0 Solving -165 + -2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '165' to each side of the equation. -165 + -2x + 165 + x2 = 0 + 165 Reorder the terms: -165 + 165 + -2x + x2 = 0 + 165 Combine like terms: -165 + 165 = 0 0 + -2x + x2 = 0 + 165 -2x + x2 = 0 + 165 Combine like terms: 0 + 165 = 165 -2x + x2 = 165 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 165 + 1 Reorder the terms: 1 + -2x + x2 = 165 + 1 Combine like terms: 165 + 1 = 166 1 + -2x + x2 = 166 Factor a perfect square on the left side: (x + -1)(x + -1) = 166 Calculate the square root of the right side: 12.884098727 Break this problem into two subproblems by setting (x + -1) equal to 12.884098727 and -12.884098727.Subproblem 1
x + -1 = 12.884098727 Simplifying x + -1 = 12.884098727 Reorder the terms: -1 + x = 12.884098727 Solving -1 + x = 12.884098727 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 12.884098727 + 1 Combine like terms: -1 + 1 = 0 0 + x = 12.884098727 + 1 x = 12.884098727 + 1 Combine like terms: 12.884098727 + 1 = 13.884098727 x = 13.884098727 Simplifying x = 13.884098727Subproblem 2
x + -1 = -12.884098727 Simplifying x + -1 = -12.884098727 Reorder the terms: -1 + x = -12.884098727 Solving -1 + x = -12.884098727 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -12.884098727 + 1 Combine like terms: -1 + 1 = 0 0 + x = -12.884098727 + 1 x = -12.884098727 + 1 Combine like terms: -12.884098727 + 1 = -11.884098727 x = -11.884098727 Simplifying x = -11.884098727Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.884098727, -11.884098727}
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