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Simplifying y2 + -16y + -64 = 0 Reorder the terms: -64 + -16y + y2 = 0 Solving -64 + -16y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '64' to each side of the equation. -64 + -16y + 64 + y2 = 0 + 64 Reorder the terms: -64 + 64 + -16y + y2 = 0 + 64 Combine like terms: -64 + 64 = 0 0 + -16y + y2 = 0 + 64 -16y + y2 = 0 + 64 Combine like terms: 0 + 64 = 64 -16y + y2 = 64 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 = 64 + 64 Reorder the terms: 64 + -16y + y2 = 64 + 64 Combine like terms: 64 + 64 = 128 64 + -16y + y2 = 128 Factor a perfect square on the left side: (y + -8)(y + -8) = 128 Calculate the square root of the right side: 11.313708499 Break this problem into two subproblems by setting (y + -8) equal to 11.313708499 and -11.313708499.Subproblem 1
y + -8 = 11.313708499 Simplifying y + -8 = 11.313708499 Reorder the terms: -8 + y = 11.313708499 Solving -8 + y = 11.313708499 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 = 11.313708499 + 8 Combine like terms: -8 + 8 = 0 0 + y = 11.313708499 + 8 y = 11.313708499 + 8 Combine like terms: 11.313708499 + 8 = 19.313708499 y = 19.313708499 Simplifying y = 19.313708499Subproblem 2
y + -8 = -11.313708499 Simplifying y + -8 = -11.313708499 Reorder the terms: -8 + y = -11.313708499 Solving -8 + y = -11.313708499 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 = -11.313708499 + 8 Combine like terms: -8 + 8 = 0 0 + y = -11.313708499 + 8 y = -11.313708499 + 8 Combine like terms: -11.313708499 + 8 = -3.313708499 y = -3.313708499 Simplifying y = -3.313708499Solution
The solution to the problem is based on the solutions from the subproblems. y = {19.313708499, -3.313708499}
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