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Simplifying (x + -1)(x + -1) = 162 Reorder the terms: (-1 + x)(x + -1) = 162 Reorder the terms: (-1 + x)(-1 + x) = 162 Multiply (-1 + x) * (-1 + x) (-1(-1 + x) + x(-1 + x)) = 162 ((-1 * -1 + x * -1) + x(-1 + x)) = 162 ((1 + -1x) + x(-1 + x)) = 162 (1 + -1x + (-1 * x + x * x)) = 162 (1 + -1x + (-1x + x2)) = 162 Combine like terms: -1x + -1x = -2x (1 + -2x + x2) = 162 Solving 1 + -2x + x2 = 162 Solving for variable 'x'. Reorder the terms: 1 + -162 + -2x + x2 = 162 + -162 Combine like terms: 1 + -162 = -161 -161 + -2x + x2 = 162 + -162 Combine like terms: 162 + -162 = 0 -161 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '161' to each side of the equation. -161 + -2x + 161 + x2 = 0 + 161 Reorder the terms: -161 + 161 + -2x + x2 = 0 + 161 Combine like terms: -161 + 161 = 0 0 + -2x + x2 = 0 + 161 -2x + x2 = 0 + 161 Combine like terms: 0 + 161 = 161 -2x + x2 = 161 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 = 161 + 1 Reorder the terms: 1 + -2x + x2 = 161 + 1 Combine like terms: 161 + 1 = 162 1 + -2x + x2 = 162 Factor a perfect square on the left side: (x + -1)(x + -1) = 162 Calculate the square root of the right side: 12.727922061 Break this problem into two subproblems by setting (x + -1) equal to 12.727922061 and -12.727922061.Subproblem 1
x + -1 = 12.727922061 Simplifying x + -1 = 12.727922061 Reorder the terms: -1 + x = 12.727922061 Solving -1 + x = 12.727922061 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 = 12.727922061 + 1 Combine like terms: -1 + 1 = 0 0 + x = 12.727922061 + 1 x = 12.727922061 + 1 Combine like terms: 12.727922061 + 1 = 13.727922061 x = 13.727922061 Simplifying x = 13.727922061Subproblem 2
x + -1 = -12.727922061 Simplifying x + -1 = -12.727922061 Reorder the terms: -1 + x = -12.727922061 Solving -1 + x = -12.727922061 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 = -12.727922061 + 1 Combine like terms: -1 + 1 = 0 0 + x = -12.727922061 + 1 x = -12.727922061 + 1 Combine like terms: -12.727922061 + 1 = -11.727922061 x = -11.727922061 Simplifying x = -11.727922061Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.727922061, -11.727922061}
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