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Simplifying (x + -5)(x + 1) = 161 Reorder the terms: (-5 + x)(x + 1) = 161 Reorder the terms: (-5 + x)(1 + x) = 161 Multiply (-5 + x) * (1 + x) (-5(1 + x) + x(1 + x)) = 161 ((1 * -5 + x * -5) + x(1 + x)) = 161 ((-5 + -5x) + x(1 + x)) = 161 (-5 + -5x + (1 * x + x * x)) = 161 (-5 + -5x + (1x + x2)) = 161 Combine like terms: -5x + 1x = -4x (-5 + -4x + x2) = 161 Solving -5 + -4x + x2 = 161 Solving for variable 'x'. Reorder the terms: -5 + -161 + -4x + x2 = 161 + -161 Combine like terms: -5 + -161 = -166 -166 + -4x + x2 = 161 + -161 Combine like terms: 161 + -161 = 0 -166 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '166' to each side of the equation. -166 + -4x + 166 + x2 = 0 + 166 Reorder the terms: -166 + 166 + -4x + x2 = 0 + 166 Combine like terms: -166 + 166 = 0 0 + -4x + x2 = 0 + 166 -4x + x2 = 0 + 166 Combine like terms: 0 + 166 = 166 -4x + x2 = 166 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 = 166 + 4 Reorder the terms: 4 + -4x + x2 = 166 + 4 Combine like terms: 166 + 4 = 170 4 + -4x + x2 = 170 Factor a perfect square on the left side: (x + -2)(x + -2) = 170 Calculate the square root of the right side: 13.03840481 Break this problem into two subproblems by setting (x + -2) equal to 13.03840481 and -13.03840481.Subproblem 1
x + -2 = 13.03840481 Simplifying x + -2 = 13.03840481 Reorder the terms: -2 + x = 13.03840481 Solving -2 + x = 13.03840481 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 = 13.03840481 + 2 Combine like terms: -2 + 2 = 0 0 + x = 13.03840481 + 2 x = 13.03840481 + 2 Combine like terms: 13.03840481 + 2 = 15.03840481 x = 15.03840481 Simplifying x = 15.03840481Subproblem 2
x + -2 = -13.03840481 Simplifying x + -2 = -13.03840481 Reorder the terms: -2 + x = -13.03840481 Solving -2 + x = -13.03840481 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 = -13.03840481 + 2 Combine like terms: -2 + 2 = 0 0 + x = -13.03840481 + 2 x = -13.03840481 + 2 Combine like terms: -13.03840481 + 2 = -11.03840481 x = -11.03840481 Simplifying x = -11.03840481Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.03840481, -11.03840481}
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