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Simplifying 2y2 + 11y + -2 = y2 + 16 Reorder the terms: -2 + 11y + 2y2 = y2 + 16 Reorder the terms: -2 + 11y + 2y2 = 16 + y2 Solving -2 + 11y + 2y2 = 16 + y2 Solving for variable 'y'. Reorder the terms: -2 + -16 + 11y + 2y2 + -1y2 = 16 + y2 + -16 + -1y2 Combine like terms: -2 + -16 = -18 -18 + 11y + 2y2 + -1y2 = 16 + y2 + -16 + -1y2 Combine like terms: 2y2 + -1y2 = 1y2 -18 + 11y + 1y2 = 16 + y2 + -16 + -1y2 Reorder the terms: -18 + 11y + 1y2 = 16 + -16 + y2 + -1y2 Combine like terms: 16 + -16 = 0 -18 + 11y + 1y2 = 0 + y2 + -1y2 -18 + 11y + 1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 -18 + 11y + 1y2 = 0 Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + 11y + 18 + y2 = 0 + 18 Reorder the terms: -18 + 18 + 11y + y2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + 11y + y2 = 0 + 18 11y + y2 = 0 + 18 Combine like terms: 0 + 18 = 18 11y + y2 = 18 The y term is 11y. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11y + 30.25 + y2 = 18 + 30.25 Reorder the terms: 30.25 + 11y + y2 = 18 + 30.25 Combine like terms: 18 + 30.25 = 48.25 30.25 + 11y + y2 = 48.25 Factor a perfect square on the left side: (y + 5.5)(y + 5.5) = 48.25 Calculate the square root of the right side: 6.946221995 Break this problem into two subproblems by setting (y + 5.5) equal to 6.946221995 and -6.946221995.Subproblem 1
y + 5.5 = 6.946221995 Simplifying y + 5.5 = 6.946221995 Reorder the terms: 5.5 + y = 6.946221995 Solving 5.5 + y = 6.946221995 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + y = 6.946221995 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + y = 6.946221995 + -5.5 y = 6.946221995 + -5.5 Combine like terms: 6.946221995 + -5.5 = 1.446221995 y = 1.446221995 Simplifying y = 1.446221995Subproblem 2
y + 5.5 = -6.946221995 Simplifying y + 5.5 = -6.946221995 Reorder the terms: 5.5 + y = -6.946221995 Solving 5.5 + y = -6.946221995 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + y = -6.946221995 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + y = -6.946221995 + -5.5 y = -6.946221995 + -5.5 Combine like terms: -6.946221995 + -5.5 = -12.446221995 y = -12.446221995 Simplifying y = -12.446221995Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.446221995, -12.446221995}
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