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Simplifying y2 + y + -128 = 0 Reorder the terms: -128 + y + y2 = 0 Solving -128 + y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '128' to each side of the equation. -128 + y + 128 + y2 = 0 + 128 Reorder the terms: -128 + 128 + y + y2 = 0 + 128 Combine like terms: -128 + 128 = 0 0 + y + y2 = 0 + 128 y + y2 = 0 + 128 Combine like terms: 0 + 128 = 128 y + y2 = 128 The y term is y. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. y + 0.25 + y2 = 128 + 0.25 Reorder the terms: 0.25 + y + y2 = 128 + 0.25 Combine like terms: 128 + 0.25 = 128.25 0.25 + y + y2 = 128.25 Factor a perfect square on the left side: (y + 0.5)(y + 0.5) = 128.25 Calculate the square root of the right side: 11.324751653 Break this problem into two subproblems by setting (y + 0.5) equal to 11.324751653 and -11.324751653.Subproblem 1
y + 0.5 = 11.324751653 Simplifying y + 0.5 = 11.324751653 Reorder the terms: 0.5 + y = 11.324751653 Solving 0.5 + y = 11.324751653 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + y = 11.324751653 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = 11.324751653 + -0.5 y = 11.324751653 + -0.5 Combine like terms: 11.324751653 + -0.5 = 10.824751653 y = 10.824751653 Simplifying y = 10.824751653Subproblem 2
y + 0.5 = -11.324751653 Simplifying y + 0.5 = -11.324751653 Reorder the terms: 0.5 + y = -11.324751653 Solving 0.5 + y = -11.324751653 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + y = -11.324751653 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = -11.324751653 + -0.5 y = -11.324751653 + -0.5 Combine like terms: -11.324751653 + -0.5 = -11.824751653 y = -11.824751653 Simplifying y = -11.824751653Solution
The solution to the problem is based on the solutions from the subproblems. y = {10.824751653, -11.824751653}
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