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Simplifying 2y2 + 8y + 16 = 361 Reorder the terms: 16 + 8y + 2y2 = 361 Solving 16 + 8y + 2y2 = 361 Solving for variable 'y'. Reorder the terms: 16 + -361 + 8y + 2y2 = 361 + -361 Combine like terms: 16 + -361 = -345 -345 + 8y + 2y2 = 361 + -361 Combine like terms: 361 + -361 = 0 -345 + 8y + 2y2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -172.5 + 4y + y2 = 0 Move the constant term to the right: Add '172.5' to each side of the equation. -172.5 + 4y + 172.5 + y2 = 0 + 172.5 Reorder the terms: -172.5 + 172.5 + 4y + y2 = 0 + 172.5 Combine like terms: -172.5 + 172.5 = 0.0 0.0 + 4y + y2 = 0 + 172.5 4y + y2 = 0 + 172.5 Combine like terms: 0 + 172.5 = 172.5 4y + y2 = 172.5 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 = 172.5 + 4 Reorder the terms: 4 + 4y + y2 = 172.5 + 4 Combine like terms: 172.5 + 4 = 176.5 4 + 4y + y2 = 176.5 Factor a perfect square on the left side: (y + 2)(y + 2) = 176.5 Calculate the square root of the right side: 13.285330256 Break this problem into two subproblems by setting (y + 2) equal to 13.285330256 and -13.285330256.Subproblem 1
y + 2 = 13.285330256 Simplifying y + 2 = 13.285330256 Reorder the terms: 2 + y = 13.285330256 Solving 2 + y = 13.285330256 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 = 13.285330256 + -2 Combine like terms: 2 + -2 = 0 0 + y = 13.285330256 + -2 y = 13.285330256 + -2 Combine like terms: 13.285330256 + -2 = 11.285330256 y = 11.285330256 Simplifying y = 11.285330256Subproblem 2
y + 2 = -13.285330256 Simplifying y + 2 = -13.285330256 Reorder the terms: 2 + y = -13.285330256 Solving 2 + y = -13.285330256 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 = -13.285330256 + -2 Combine like terms: 2 + -2 = 0 0 + y = -13.285330256 + -2 y = -13.285330256 + -2 Combine like terms: -13.285330256 + -2 = -15.285330256 y = -15.285330256 Simplifying y = -15.285330256Solution
The solution to the problem is based on the solutions from the subproblems. y = {11.285330256, -15.285330256}
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