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Simplifying y2 + 11y + -100 = 0 Reorder the terms: -100 + 11y + y2 = 0 Solving -100 + 11y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '100' to each side of the equation. -100 + 11y + 100 + y2 = 0 + 100 Reorder the terms: -100 + 100 + 11y + y2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + 11y + y2 = 0 + 100 11y + y2 = 0 + 100 Combine like terms: 0 + 100 = 100 11y + y2 = 100 The y term is 11y. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11y + 30.25 + y2 = 100 + 30.25 Reorder the terms: 30.25 + 11y + y2 = 100 + 30.25 Combine like terms: 100 + 30.25 = 130.25 30.25 + 11y + y2 = 130.25 Factor a perfect square on the left side: (y + 5.5)(y + 5.5) = 130.25 Calculate the square root of the right side: 11.412712211 Break this problem into two subproblems by setting (y + 5.5) equal to 11.412712211 and -11.412712211.Subproblem 1
y + 5.5 = 11.412712211 Simplifying y + 5.5 = 11.412712211 Reorder the terms: 5.5 + y = 11.412712211 Solving 5.5 + y = 11.412712211 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + y = 11.412712211 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + y = 11.412712211 + -5.5 y = 11.412712211 + -5.5 Combine like terms: 11.412712211 + -5.5 = 5.912712211 y = 5.912712211 Simplifying y = 5.912712211Subproblem 2
y + 5.5 = -11.412712211 Simplifying y + 5.5 = -11.412712211 Reorder the terms: 5.5 + y = -11.412712211 Solving 5.5 + y = -11.412712211 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + y = -11.412712211 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + y = -11.412712211 + -5.5 y = -11.412712211 + -5.5 Combine like terms: -11.412712211 + -5.5 = -16.912712211 y = -16.912712211 Simplifying y = -16.912712211Solution
The solution to the problem is based on the solutions from the subproblems. y = {5.912712211, -16.912712211}
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