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Simplifying y2 + 16y = -2 Reorder the terms: 16y + y2 = -2 Solving 16y + y2 = -2 Solving for variable 'y'. Reorder the terms: 2 + 16y + y2 = -2 + 2 Combine like terms: -2 + 2 = 0 2 + 16y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + 16y + -2 + y2 = 0 + -2 Reorder the terms: 2 + -2 + 16y + y2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 16y + y2 = 0 + -2 16y + y2 = 0 + -2 Combine like terms: 0 + -2 = -2 16y + y2 = -2 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 = -2 + 64 Reorder the terms: 64 + 16y + y2 = -2 + 64 Combine like terms: -2 + 64 = 62 64 + 16y + y2 = 62 Factor a perfect square on the left side: (y + 8)(y + 8) = 62 Calculate the square root of the right side: 7.874007874 Break this problem into two subproblems by setting (y + 8) equal to 7.874007874 and -7.874007874.Subproblem 1
y + 8 = 7.874007874 Simplifying y + 8 = 7.874007874 Reorder the terms: 8 + y = 7.874007874 Solving 8 + y = 7.874007874 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 = 7.874007874 + -8 Combine like terms: 8 + -8 = 0 0 + y = 7.874007874 + -8 y = 7.874007874 + -8 Combine like terms: 7.874007874 + -8 = -0.125992126 y = -0.125992126 Simplifying y = -0.125992126Subproblem 2
y + 8 = -7.874007874 Simplifying y + 8 = -7.874007874 Reorder the terms: 8 + y = -7.874007874 Solving 8 + y = -7.874007874 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 = -7.874007874 + -8 Combine like terms: 8 + -8 = 0 0 + y = -7.874007874 + -8 y = -7.874007874 + -8 Combine like terms: -7.874007874 + -8 = -15.874007874 y = -15.874007874 Simplifying y = -15.874007874Solution
The solution to the problem is based on the solutions from the subproblems. y = {-0.125992126, -15.874007874}
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