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Simplifying 11y = y2 + 20 Reorder the terms: 11y = 20 + y2 Solving 11y = 20 + y2 Solving for variable 'y'. Reorder the terms: -20 + 11y + -1y2 = 20 + y2 + -20 + -1y2 Reorder the terms: -20 + 11y + -1y2 = 20 + -20 + y2 + -1y2 Combine like terms: 20 + -20 = 0 -20 + 11y + -1y2 = 0 + y2 + -1y2 -20 + 11y + -1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 -20 + 11y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 20 + -11y + y2 = 0 Move the constant term to the right: Add '-20' to each side of the equation. 20 + -11y + -20 + y2 = 0 + -20 Reorder the terms: 20 + -20 + -11y + y2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -11y + y2 = 0 + -20 -11y + y2 = 0 + -20 Combine like terms: 0 + -20 = -20 -11y + y2 = -20 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 = -20 + 30.25 Reorder the terms: 30.25 + -11y + y2 = -20 + 30.25 Combine like terms: -20 + 30.25 = 10.25 30.25 + -11y + y2 = 10.25 Factor a perfect square on the left side: (y + -5.5)(y + -5.5) = 10.25 Calculate the square root of the right side: 3.201562119 Break this problem into two subproblems by setting (y + -5.5) equal to 3.201562119 and -3.201562119.Subproblem 1
y + -5.5 = 3.201562119 Simplifying y + -5.5 = 3.201562119 Reorder the terms: -5.5 + y = 3.201562119 Solving -5.5 + y = 3.201562119 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 = 3.201562119 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + y = 3.201562119 + 5.5 y = 3.201562119 + 5.5 Combine like terms: 3.201562119 + 5.5 = 8.701562119 y = 8.701562119 Simplifying y = 8.701562119Subproblem 2
y + -5.5 = -3.201562119 Simplifying y + -5.5 = -3.201562119 Reorder the terms: -5.5 + y = -3.201562119 Solving -5.5 + y = -3.201562119 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 = -3.201562119 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + y = -3.201562119 + 5.5 y = -3.201562119 + 5.5 Combine like terms: -3.201562119 + 5.5 = 2.298437881 y = 2.298437881 Simplifying y = 2.298437881Solution
The solution to the problem is based on the solutions from the subproblems. y = {8.701562119, 2.298437881}
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