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Simplifying 2y2 + -14y + 28 = y2 + -36y + 36 Reorder the terms: 28 + -14y + 2y2 = y2 + -36y + 36 Reorder the terms: 28 + -14y + 2y2 = 36 + -36y + y2 Solving 28 + -14y + 2y2 = 36 + -36y + y2 Solving for variable 'y'. Reorder the terms: 28 + -36 + -14y + 36y + 2y2 + -1y2 = 36 + -36y + y2 + -36 + 36y + -1y2 Combine like terms: 28 + -36 = -8 -8 + -14y + 36y + 2y2 + -1y2 = 36 + -36y + y2 + -36 + 36y + -1y2 Combine like terms: -14y + 36y = 22y -8 + 22y + 2y2 + -1y2 = 36 + -36y + y2 + -36 + 36y + -1y2 Combine like terms: 2y2 + -1y2 = 1y2 -8 + 22y + 1y2 = 36 + -36y + y2 + -36 + 36y + -1y2 Reorder the terms: -8 + 22y + 1y2 = 36 + -36 + -36y + 36y + y2 + -1y2 Combine like terms: 36 + -36 = 0 -8 + 22y + 1y2 = 0 + -36y + 36y + y2 + -1y2 -8 + 22y + 1y2 = -36y + 36y + y2 + -1y2 Combine like terms: -36y + 36y = 0 -8 + 22y + 1y2 = 0 + y2 + -1y2 -8 + 22y + 1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 -8 + 22y + 1y2 = 0 Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + 22y + 8 + y2 = 0 + 8 Reorder the terms: -8 + 8 + 22y + y2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 22y + y2 = 0 + 8 22y + y2 = 0 + 8 Combine like terms: 0 + 8 = 8 22y + y2 = 8 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 = 8 + 121 Reorder the terms: 121 + 22y + y2 = 8 + 121 Combine like terms: 8 + 121 = 129 121 + 22y + y2 = 129 Factor a perfect square on the left side: (y + 11)(y + 11) = 129 Calculate the square root of the right side: 11.357816692 Break this problem into two subproblems by setting (y + 11) equal to 11.357816692 and -11.357816692.Subproblem 1
y + 11 = 11.357816692 Simplifying y + 11 = 11.357816692 Reorder the terms: 11 + y = 11.357816692 Solving 11 + y = 11.357816692 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 = 11.357816692 + -11 Combine like terms: 11 + -11 = 0 0 + y = 11.357816692 + -11 y = 11.357816692 + -11 Combine like terms: 11.357816692 + -11 = 0.357816692 y = 0.357816692 Simplifying y = 0.357816692Subproblem 2
y + 11 = -11.357816692 Simplifying y + 11 = -11.357816692 Reorder the terms: 11 + y = -11.357816692 Solving 11 + y = -11.357816692 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 = -11.357816692 + -11 Combine like terms: 11 + -11 = 0 0 + y = -11.357816692 + -11 y = -11.357816692 + -11 Combine like terms: -11.357816692 + -11 = -22.357816692 y = -22.357816692 Simplifying y = -22.357816692Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.357816692, -22.357816692}
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