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Simplifying y2 + -4y = 161 Reorder the terms: -4y + y2 = 161 Solving -4y + y2 = 161 Solving for variable 'y'. Reorder the terms: -161 + -4y + y2 = 161 + -161 Combine like terms: 161 + -161 = 0 -161 + -4y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '161' to each side of the equation. -161 + -4y + 161 + y2 = 0 + 161 Reorder the terms: -161 + 161 + -4y + y2 = 0 + 161 Combine like terms: -161 + 161 = 0 0 + -4y + y2 = 0 + 161 -4y + y2 = 0 + 161 Combine like terms: 0 + 161 = 161 -4y + y2 = 161 The y term is -4y. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4y + 4 + y2 = 161 + 4 Reorder the terms: 4 + -4y + y2 = 161 + 4 Combine like terms: 161 + 4 = 165 4 + -4y + y2 = 165 Factor a perfect square on the left side: (y + -2)(y + -2) = 165 Calculate the square root of the right side: 12.845232579 Break this problem into two subproblems by setting (y + -2) equal to 12.845232579 and -12.845232579.Subproblem 1
y + -2 = 12.845232579 Simplifying y + -2 = 12.845232579 Reorder the terms: -2 + y = 12.845232579 Solving -2 + y = 12.845232579 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + y = 12.845232579 + 2 Combine like terms: -2 + 2 = 0 0 + y = 12.845232579 + 2 y = 12.845232579 + 2 Combine like terms: 12.845232579 + 2 = 14.845232579 y = 14.845232579 Simplifying y = 14.845232579Subproblem 2
y + -2 = -12.845232579 Simplifying y + -2 = -12.845232579 Reorder the terms: -2 + y = -12.845232579 Solving -2 + y = -12.845232579 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + y = -12.845232579 + 2 Combine like terms: -2 + 2 = 0 0 + y = -12.845232579 + 2 y = -12.845232579 + 2 Combine like terms: -12.845232579 + 2 = -10.845232579 y = -10.845232579 Simplifying y = -10.845232579Solution
The solution to the problem is based on the solutions from the subproblems. y = {14.845232579, -10.845232579}
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