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Simplifying y2 + -22y = -23 Reorder the terms: -22y + y2 = -23 Solving -22y + y2 = -23 Solving for variable 'y'. Reorder the terms: 23 + -22y + y2 = -23 + 23 Combine like terms: -23 + 23 = 0 23 + -22y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-23' to each side of the equation. 23 + -22y + -23 + y2 = 0 + -23 Reorder the terms: 23 + -23 + -22y + y2 = 0 + -23 Combine like terms: 23 + -23 = 0 0 + -22y + y2 = 0 + -23 -22y + y2 = 0 + -23 Combine like terms: 0 + -23 = -23 -22y + y2 = -23 The y term is -22y. Take half its coefficient (-11). Square it (121) and add it to both sides. Add '121' to each side of the equation. -22y + 121 + y2 = -23 + 121 Reorder the terms: 121 + -22y + y2 = -23 + 121 Combine like terms: -23 + 121 = 98 121 + -22y + y2 = 98 Factor a perfect square on the left side: (y + -11)(y + -11) = 98 Calculate the square root of the right side: 9.899494937 Break this problem into two subproblems by setting (y + -11) equal to 9.899494937 and -9.899494937.Subproblem 1
y + -11 = 9.899494937 Simplifying y + -11 = 9.899494937 Reorder the terms: -11 + y = 9.899494937 Solving -11 + y = 9.899494937 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + y = 9.899494937 + 11 Combine like terms: -11 + 11 = 0 0 + y = 9.899494937 + 11 y = 9.899494937 + 11 Combine like terms: 9.899494937 + 11 = 20.899494937 y = 20.899494937 Simplifying y = 20.899494937Subproblem 2
y + -11 = -9.899494937 Simplifying y + -11 = -9.899494937 Reorder the terms: -11 + y = -9.899494937 Solving -11 + y = -9.899494937 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + y = -9.899494937 + 11 Combine like terms: -11 + 11 = 0 0 + y = -9.899494937 + 11 y = -9.899494937 + 11 Combine like terms: -9.899494937 + 11 = 1.100505063 y = 1.100505063 Simplifying y = 1.100505063Solution
The solution to the problem is based on the solutions from the subproblems. y = {20.899494937, 1.100505063}
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