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Simplifying 23y + -1y2 = 2 Solving 23y + -1y2 = 2 Solving for variable 'y'. Reorder the terms: -2 + 23y + -1y2 = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + 23y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 2 + -23y + y2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -23y + -2 + y2 = 0 + -2 Reorder the terms: 2 + -2 + -23y + y2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -23y + y2 = 0 + -2 -23y + y2 = 0 + -2 Combine like terms: 0 + -2 = -2 -23y + y2 = -2 The y term is -23y. Take half its coefficient (-11.5). Square it (132.25) and add it to both sides. Add '132.25' to each side of the equation. -23y + 132.25 + y2 = -2 + 132.25 Reorder the terms: 132.25 + -23y + y2 = -2 + 132.25 Combine like terms: -2 + 132.25 = 130.25 132.25 + -23y + y2 = 130.25 Factor a perfect square on the left side: (y + -11.5)(y + -11.5) = 130.25 Calculate the square root of the right side: 11.412712211 Break this problem into two subproblems by setting (y + -11.5) equal to 11.412712211 and -11.412712211.Subproblem 1
y + -11.5 = 11.412712211 Simplifying y + -11.5 = 11.412712211 Reorder the terms: -11.5 + y = 11.412712211 Solving -11.5 + y = 11.412712211 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '11.5' to each side of the equation. -11.5 + 11.5 + y = 11.412712211 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + y = 11.412712211 + 11.5 y = 11.412712211 + 11.5 Combine like terms: 11.412712211 + 11.5 = 22.912712211 y = 22.912712211 Simplifying y = 22.912712211Subproblem 2
y + -11.5 = -11.412712211 Simplifying y + -11.5 = -11.412712211 Reorder the terms: -11.5 + y = -11.412712211 Solving -11.5 + y = -11.412712211 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '11.5' to each side of the equation. -11.5 + 11.5 + y = -11.412712211 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + y = -11.412712211 + 11.5 y = -11.412712211 + 11.5 Combine like terms: -11.412712211 + 11.5 = 0.087287789 y = 0.087287789 Simplifying y = 0.087287789Solution
The solution to the problem is based on the solutions from the subproblems. y = {22.912712211, 0.087287789}
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