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Simplifying y2 + 16y = 163 Reorder the terms: 16y + y2 = 163 Solving 16y + y2 = 163 Solving for variable 'y'. Reorder the terms: -163 + 16y + y2 = 163 + -163 Combine like terms: 163 + -163 = 0 -163 + 16y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '163' to each side of the equation. -163 + 16y + 163 + y2 = 0 + 163 Reorder the terms: -163 + 163 + 16y + y2 = 0 + 163 Combine like terms: -163 + 163 = 0 0 + 16y + y2 = 0 + 163 16y + y2 = 0 + 163 Combine like terms: 0 + 163 = 163 16y + y2 = 163 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 = 163 + 64 Reorder the terms: 64 + 16y + y2 = 163 + 64 Combine like terms: 163 + 64 = 227 64 + 16y + y2 = 227 Factor a perfect square on the left side: (y + 8)(y + 8) = 227 Calculate the square root of the right side: 15.066519173 Break this problem into two subproblems by setting (y + 8) equal to 15.066519173 and -15.066519173.Subproblem 1
y + 8 = 15.066519173 Simplifying y + 8 = 15.066519173 Reorder the terms: 8 + y = 15.066519173 Solving 8 + y = 15.066519173 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 = 15.066519173 + -8 Combine like terms: 8 + -8 = 0 0 + y = 15.066519173 + -8 y = 15.066519173 + -8 Combine like terms: 15.066519173 + -8 = 7.066519173 y = 7.066519173 Simplifying y = 7.066519173Subproblem 2
y + 8 = -15.066519173 Simplifying y + 8 = -15.066519173 Reorder the terms: 8 + y = -15.066519173 Solving 8 + y = -15.066519173 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 = -15.066519173 + -8 Combine like terms: 8 + -8 = 0 0 + y = -15.066519173 + -8 y = -15.066519173 + -8 Combine like terms: -15.066519173 + -8 = -23.066519173 y = -23.066519173 Simplifying y = -23.066519173Solution
The solution to the problem is based on the solutions from the subproblems. y = {7.066519173, -23.066519173}
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