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Simplifying y^{2}+ -16y + -4 = 0 Reorder the terms: -4 + -16y + y^{2}= 0 Solving -4 + -16y + y^{2}= 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + -16y + 4 + y^{2}= 0 + 4 Reorder the terms: -4 + 4 + -16y + y^{2}= 0 + 4 Combine like terms: -4 + 4 = 0 0 + -16y + y^{2}= 0 + 4 -16y + y^{2}= 0 + 4 Combine like terms: 0 + 4 = 4 -16y + y^{2}= 4 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 + y^{2}= 4 + 64 Reorder the terms: 64 + -16y + y^{2}= 4 + 64 Combine like terms: 4 + 64 = 68 64 + -16y + y^{2}= 68 Factor a perfect square on the left side: (y + -8)(y + -8) = 68 Calculate the square root of the right side: 8.246211251 Break this problem into two subproblems by setting (y + -8) equal to 8.246211251 and -8.246211251.## Subproblem 1

y + -8 = 8.246211251 Simplifying y + -8 = 8.246211251 Reorder the terms: -8 + y = 8.246211251 Solving -8 + y = 8.246211251 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 = 8.246211251 + 8 Combine like terms: -8 + 8 = 0 0 + y = 8.246211251 + 8 y = 8.246211251 + 8 Combine like terms: 8.246211251 + 8 = 16.246211251 y = 16.246211251 Simplifying y = 16.246211251## Subproblem 2

y + -8 = -8.246211251 Simplifying y + -8 = -8.246211251 Reorder the terms: -8 + y = -8.246211251 Solving -8 + y = -8.246211251 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 = -8.246211251 + 8 Combine like terms: -8 + 8 = 0 0 + y = -8.246211251 + 8 y = -8.246211251 + 8 Combine like terms: -8.246211251 + 8 = -0.246211251 y = -0.246211251 Simplifying y = -0.246211251## Solution

The solution to the problem is based on the solutions from the subproblems. y = {16.246211251, -0.246211251}

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