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Simplifying y2 + 16y = -3 Reorder the terms: 16y + y2 = -3 Solving 16y + y2 = -3 Solving for variable 'y'. Reorder the terms: 3 + 16y + y2 = -3 + 3 Combine like terms: -3 + 3 = 0 3 + 16y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + 16y + -3 + y2 = 0 + -3 Reorder the terms: 3 + -3 + 16y + y2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 16y + y2 = 0 + -3 16y + y2 = 0 + -3 Combine like terms: 0 + -3 = -3 16y + y2 = -3 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 = -3 + 64 Reorder the terms: 64 + 16y + y2 = -3 + 64 Combine like terms: -3 + 64 = 61 64 + 16y + y2 = 61 Factor a perfect square on the left side: (y + 8)(y + 8) = 61 Calculate the square root of the right side: 7.810249676 Break this problem into two subproblems by setting (y + 8) equal to 7.810249676 and -7.810249676.Subproblem 1
y + 8 = 7.810249676 Simplifying y + 8 = 7.810249676 Reorder the terms: 8 + y = 7.810249676 Solving 8 + y = 7.810249676 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 = 7.810249676 + -8 Combine like terms: 8 + -8 = 0 0 + y = 7.810249676 + -8 y = 7.810249676 + -8 Combine like terms: 7.810249676 + -8 = -0.189750324 y = -0.189750324 Simplifying y = -0.189750324Subproblem 2
y + 8 = -7.810249676 Simplifying y + 8 = -7.810249676 Reorder the terms: 8 + y = -7.810249676 Solving 8 + y = -7.810249676 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 = -7.810249676 + -8 Combine like terms: 8 + -8 = 0 0 + y = -7.810249676 + -8 y = -7.810249676 + -8 Combine like terms: -7.810249676 + -8 = -15.810249676 y = -15.810249676 Simplifying y = -15.810249676Solution
The solution to the problem is based on the solutions from the subproblems. y = {-0.189750324, -15.810249676}
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