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Simplifying y2 + -16y = 55 Reorder the terms: -16y + y2 = 55 Solving -16y + y2 = 55 Solving for variable 'y'. Reorder the terms: -55 + -16y + y2 = 55 + -55 Combine like terms: 55 + -55 = 0 -55 + -16y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '55' to each side of the equation. -55 + -16y + 55 + y2 = 0 + 55 Reorder the terms: -55 + 55 + -16y + y2 = 0 + 55 Combine like terms: -55 + 55 = 0 0 + -16y + y2 = 0 + 55 -16y + y2 = 0 + 55 Combine like terms: 0 + 55 = 55 -16y + y2 = 55 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 = 55 + 64 Reorder the terms: 64 + -16y + y2 = 55 + 64 Combine like terms: 55 + 64 = 119 64 + -16y + y2 = 119 Factor a perfect square on the left side: (y + -8)(y + -8) = 119 Calculate the square root of the right side: 10.908712115 Break this problem into two subproblems by setting (y + -8) equal to 10.908712115 and -10.908712115.Subproblem 1
y + -8 = 10.908712115 Simplifying y + -8 = 10.908712115 Reorder the terms: -8 + y = 10.908712115 Solving -8 + y = 10.908712115 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 = 10.908712115 + 8 Combine like terms: -8 + 8 = 0 0 + y = 10.908712115 + 8 y = 10.908712115 + 8 Combine like terms: 10.908712115 + 8 = 18.908712115 y = 18.908712115 Simplifying y = 18.908712115Subproblem 2
y + -8 = -10.908712115 Simplifying y + -8 = -10.908712115 Reorder the terms: -8 + y = -10.908712115 Solving -8 + y = -10.908712115 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 = -10.908712115 + 8 Combine like terms: -8 + 8 = 0 0 + y = -10.908712115 + 8 y = -10.908712115 + 8 Combine like terms: -10.908712115 + 8 = -2.908712115 y = -2.908712115 Simplifying y = -2.908712115Solution
The solution to the problem is based on the solutions from the subproblems. y = {18.908712115, -2.908712115}
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