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Simplifying y2 + -36y + -1600 = 0 Reorder the terms: -1600 + -36y + y2 = 0 Solving -1600 + -36y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '1600' to each side of the equation. -1600 + -36y + 1600 + y2 = 0 + 1600 Reorder the terms: -1600 + 1600 + -36y + y2 = 0 + 1600 Combine like terms: -1600 + 1600 = 0 0 + -36y + y2 = 0 + 1600 -36y + y2 = 0 + 1600 Combine like terms: 0 + 1600 = 1600 -36y + y2 = 1600 The y term is -36y. Take half its coefficient (-18). Square it (324) and add it to both sides. Add '324' to each side of the equation. -36y + 324 + y2 = 1600 + 324 Reorder the terms: 324 + -36y + y2 = 1600 + 324 Combine like terms: 1600 + 324 = 1924 324 + -36y + y2 = 1924 Factor a perfect square on the left side: (y + -18)(y + -18) = 1924 Calculate the square root of the right side: 43.863424399 Break this problem into two subproblems by setting (y + -18) equal to 43.863424399 and -43.863424399.Subproblem 1
y + -18 = 43.863424399 Simplifying y + -18 = 43.863424399 Reorder the terms: -18 + y = 43.863424399 Solving -18 + y = 43.863424399 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + y = 43.863424399 + 18 Combine like terms: -18 + 18 = 0 0 + y = 43.863424399 + 18 y = 43.863424399 + 18 Combine like terms: 43.863424399 + 18 = 61.863424399 y = 61.863424399 Simplifying y = 61.863424399Subproblem 2
y + -18 = -43.863424399 Simplifying y + -18 = -43.863424399 Reorder the terms: -18 + y = -43.863424399 Solving -18 + y = -43.863424399 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + y = -43.863424399 + 18 Combine like terms: -18 + 18 = 0 0 + y = -43.863424399 + 18 y = -43.863424399 + 18 Combine like terms: -43.863424399 + 18 = -25.863424399 y = -25.863424399 Simplifying y = -25.863424399Solution
The solution to the problem is based on the solutions from the subproblems. y = {61.863424399, -25.863424399}
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