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Simplifying y2 + -6y + -161 = 0 Reorder the terms: -161 + -6y + y2 = 0 Solving -161 + -6y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '161' to each side of the equation. -161 + -6y + 161 + y2 = 0 + 161 Reorder the terms: -161 + 161 + -6y + y2 = 0 + 161 Combine like terms: -161 + 161 = 0 0 + -6y + y2 = 0 + 161 -6y + y2 = 0 + 161 Combine like terms: 0 + 161 = 161 -6y + y2 = 161 The y term is -6y. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6y + 9 + y2 = 161 + 9 Reorder the terms: 9 + -6y + y2 = 161 + 9 Combine like terms: 161 + 9 = 170 9 + -6y + y2 = 170 Factor a perfect square on the left side: (y + -3)(y + -3) = 170 Calculate the square root of the right side: 13.03840481 Break this problem into two subproblems by setting (y + -3) equal to 13.03840481 and -13.03840481.Subproblem 1
y + -3 = 13.03840481 Simplifying y + -3 = 13.03840481 Reorder the terms: -3 + y = 13.03840481 Solving -3 + y = 13.03840481 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + y = 13.03840481 + 3 Combine like terms: -3 + 3 = 0 0 + y = 13.03840481 + 3 y = 13.03840481 + 3 Combine like terms: 13.03840481 + 3 = 16.03840481 y = 16.03840481 Simplifying y = 16.03840481Subproblem 2
y + -3 = -13.03840481 Simplifying y + -3 = -13.03840481 Reorder the terms: -3 + y = -13.03840481 Solving -3 + y = -13.03840481 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + y = -13.03840481 + 3 Combine like terms: -3 + 3 = 0 0 + y = -13.03840481 + 3 y = -13.03840481 + 3 Combine like terms: -13.03840481 + 3 = -10.03840481 y = -10.03840481 Simplifying y = -10.03840481Solution
The solution to the problem is based on the solutions from the subproblems. y = {16.03840481, -10.03840481}
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