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Simplifying y(64 + y) = 3366 (64 * y + y * y) = 3366 (64y + y2) = 3366 Solving 64y + y2 = 3366 Solving for variable 'y'. Reorder the terms: -3366 + 64y + y2 = 3366 + -3366 Combine like terms: 3366 + -3366 = 0 -3366 + 64y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '3366' to each side of the equation. -3366 + 64y + 3366 + y2 = 0 + 3366 Reorder the terms: -3366 + 3366 + 64y + y2 = 0 + 3366 Combine like terms: -3366 + 3366 = 0 0 + 64y + y2 = 0 + 3366 64y + y2 = 0 + 3366 Combine like terms: 0 + 3366 = 3366 64y + y2 = 3366 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 = 3366 + 1024 Reorder the terms: 1024 + 64y + y2 = 3366 + 1024 Combine like terms: 3366 + 1024 = 4390 1024 + 64y + y2 = 4390 Factor a perfect square on the left side: (y + 32)(y + 32) = 4390 Calculate the square root of the right side: 66.257075094 Break this problem into two subproblems by setting (y + 32) equal to 66.257075094 and -66.257075094.Subproblem 1
y + 32 = 66.257075094 Simplifying y + 32 = 66.257075094 Reorder the terms: 32 + y = 66.257075094 Solving 32 + y = 66.257075094 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 = 66.257075094 + -32 Combine like terms: 32 + -32 = 0 0 + y = 66.257075094 + -32 y = 66.257075094 + -32 Combine like terms: 66.257075094 + -32 = 34.257075094 y = 34.257075094 Simplifying y = 34.257075094Subproblem 2
y + 32 = -66.257075094 Simplifying y + 32 = -66.257075094 Reorder the terms: 32 + y = -66.257075094 Solving 32 + y = -66.257075094 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 = -66.257075094 + -32 Combine like terms: 32 + -32 = 0 0 + y = -66.257075094 + -32 y = -66.257075094 + -32 Combine like terms: -66.257075094 + -32 = -98.257075094 y = -98.257075094 Simplifying y = -98.257075094Solution
The solution to the problem is based on the solutions from the subproblems. y = {34.257075094, -98.257075094}
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