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Simplifying y2 + 64y = 512 Reorder the terms: 64y + y2 = 512 Solving 64y + y2 = 512 Solving for variable 'y'. Reorder the terms: -512 + 64y + y2 = 512 + -512 Combine like terms: 512 + -512 = 0 -512 + 64y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '512' to each side of the equation. -512 + 64y + 512 + y2 = 0 + 512 Reorder the terms: -512 + 512 + 64y + y2 = 0 + 512 Combine like terms: -512 + 512 = 0 0 + 64y + y2 = 0 + 512 64y + y2 = 0 + 512 Combine like terms: 0 + 512 = 512 64y + y2 = 512 The y term is 64y. Take half its coefficient (32). Square it (1024) and add it to both sides. Add '1024' to each side of the equation. 64y + 1024 + y2 = 512 + 1024 Reorder the terms: 1024 + 64y + y2 = 512 + 1024 Combine like terms: 512 + 1024 = 1536 1024 + 64y + y2 = 1536 Factor a perfect square on the left side: (y + 32)(y + 32) = 1536 Calculate the square root of the right side: 39.191835885 Break this problem into two subproblems by setting (y + 32) equal to 39.191835885 and -39.191835885.Subproblem 1
y + 32 = 39.191835885 Simplifying y + 32 = 39.191835885 Reorder the terms: 32 + y = 39.191835885 Solving 32 + y = 39.191835885 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-32' to each side of the equation. 32 + -32 + y = 39.191835885 + -32 Combine like terms: 32 + -32 = 0 0 + y = 39.191835885 + -32 y = 39.191835885 + -32 Combine like terms: 39.191835885 + -32 = 7.191835885 y = 7.191835885 Simplifying y = 7.191835885Subproblem 2
y + 32 = -39.191835885 Simplifying y + 32 = -39.191835885 Reorder the terms: 32 + y = -39.191835885 Solving 32 + y = -39.191835885 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-32' to each side of the equation. 32 + -32 + y = -39.191835885 + -32 Combine like terms: 32 + -32 = 0 0 + y = -39.191835885 + -32 y = -39.191835885 + -32 Combine like terms: -39.191835885 + -32 = -71.191835885 y = -71.191835885 Simplifying y = -71.191835885Solution
The solution to the problem is based on the solutions from the subproblems. y = {7.191835885, -71.191835885}
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