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Simplifying (x + -1)(x + -3) = 166 Reorder the terms: (-1 + x)(x + -3) = 166 Reorder the terms: (-1 + x)(-3 + x) = 166 Multiply (-1 + x) * (-3 + x) (-1(-3 + x) + x(-3 + x)) = 166 ((-3 * -1 + x * -1) + x(-3 + x)) = 166 ((3 + -1x) + x(-3 + x)) = 166 (3 + -1x + (-3 * x + x * x)) = 166 (3 + -1x + (-3x + x2)) = 166 Combine like terms: -1x + -3x = -4x (3 + -4x + x2) = 166 Solving 3 + -4x + x2 = 166 Solving for variable 'x'. Reorder the terms: 3 + -166 + -4x + x2 = 166 + -166 Combine like terms: 3 + -166 = -163 -163 + -4x + x2 = 166 + -166 Combine like terms: 166 + -166 = 0 -163 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '163' to each side of the equation. -163 + -4x + 163 + x2 = 0 + 163 Reorder the terms: -163 + 163 + -4x + x2 = 0 + 163 Combine like terms: -163 + 163 = 0 0 + -4x + x2 = 0 + 163 -4x + x2 = 0 + 163 Combine like terms: 0 + 163 = 163 -4x + x2 = 163 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 163 + 4 Reorder the terms: 4 + -4x + x2 = 163 + 4 Combine like terms: 163 + 4 = 167 4 + -4x + x2 = 167 Factor a perfect square on the left side: (x + -2)(x + -2) = 167 Calculate the square root of the right side: 12.922847983 Break this problem into two subproblems by setting (x + -2) equal to 12.922847983 and -12.922847983.Subproblem 1
x + -2 = 12.922847983 Simplifying x + -2 = 12.922847983 Reorder the terms: -2 + x = 12.922847983 Solving -2 + x = 12.922847983 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 12.922847983 + 2 Combine like terms: -2 + 2 = 0 0 + x = 12.922847983 + 2 x = 12.922847983 + 2 Combine like terms: 12.922847983 + 2 = 14.922847983 x = 14.922847983 Simplifying x = 14.922847983Subproblem 2
x + -2 = -12.922847983 Simplifying x + -2 = -12.922847983 Reorder the terms: -2 + x = -12.922847983 Solving -2 + x = -12.922847983 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -12.922847983 + 2 Combine like terms: -2 + 2 = 0 0 + x = -12.922847983 + 2 x = -12.922847983 + 2 Combine like terms: -12.922847983 + 2 = -10.922847983 x = -10.922847983 Simplifying x = -10.922847983Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.922847983, -10.922847983}
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