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Simplifying y2 + -16y + 61 = 81 Reorder the terms: 61 + -16y + y2 = 81 Solving 61 + -16y + y2 = 81 Solving for variable 'y'. Reorder the terms: 61 + -81 + -16y + y2 = 81 + -81 Combine like terms: 61 + -81 = -20 -20 + -16y + y2 = 81 + -81 Combine like terms: 81 + -81 = 0 -20 + -16y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '20' to each side of the equation. -20 + -16y + 20 + y2 = 0 + 20 Reorder the terms: -20 + 20 + -16y + y2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -16y + y2 = 0 + 20 -16y + y2 = 0 + 20 Combine like terms: 0 + 20 = 20 -16y + y2 = 20 The y term is -16y. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16y + 64 + y2 = 20 + 64 Reorder the terms: 64 + -16y + y2 = 20 + 64 Combine like terms: 20 + 64 = 84 64 + -16y + y2 = 84 Factor a perfect square on the left side: (y + -8)(y + -8) = 84 Calculate the square root of the right side: 9.16515139 Break this problem into two subproblems by setting (y + -8) equal to 9.16515139 and -9.16515139.Subproblem 1
y + -8 = 9.16515139 Simplifying y + -8 = 9.16515139 Reorder the terms: -8 + y = 9.16515139 Solving -8 + y = 9.16515139 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + y = 9.16515139 + 8 Combine like terms: -8 + 8 = 0 0 + y = 9.16515139 + 8 y = 9.16515139 + 8 Combine like terms: 9.16515139 + 8 = 17.16515139 y = 17.16515139 Simplifying y = 17.16515139Subproblem 2
y + -8 = -9.16515139 Simplifying y + -8 = -9.16515139 Reorder the terms: -8 + y = -9.16515139 Solving -8 + y = -9.16515139 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + y = -9.16515139 + 8 Combine like terms: -8 + 8 = 0 0 + y = -9.16515139 + 8 y = -9.16515139 + 8 Combine like terms: -9.16515139 + 8 = -1.16515139 y = -1.16515139 Simplifying y = -1.16515139Solution
The solution to the problem is based on the solutions from the subproblems. y = {17.16515139, -1.16515139}
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