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Simplifying y2 + 16y = 4 Reorder the terms: 16y + y2 = 4 Solving 16y + y2 = 4 Solving for variable 'y'. Reorder the terms: -4 + 16y + y2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + 16y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + 16y + 4 + y2 = 0 + 4 Reorder the terms: -4 + 4 + 16y + y2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 16y + y2 = 0 + 4 16y + y2 = 0 + 4 Combine like terms: 0 + 4 = 4 16y + y2 = 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 + y2 = 4 + 64 Reorder the terms: 64 + 16y + y2 = 4 + 64 Combine like terms: 4 + 64 = 68 64 + 16y + y2 = 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 = 0.246211251 y = 0.246211251 Simplifying y = 0.246211251Subproblem 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 = -16.246211251 y = -16.246211251 Simplifying y = -16.246211251Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.246211251, -16.246211251}
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