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Simplifying y2 + 2y + -22 = 0 Reorder the terms: -22 + 2y + y2 = 0 Solving -22 + 2y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '22' to each side of the equation. -22 + 2y + 22 + y2 = 0 + 22 Reorder the terms: -22 + 22 + 2y + y2 = 0 + 22 Combine like terms: -22 + 22 = 0 0 + 2y + y2 = 0 + 22 2y + y2 = 0 + 22 Combine like terms: 0 + 22 = 22 2y + y2 = 22 The y term is 2y. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2y + 1 + y2 = 22 + 1 Reorder the terms: 1 + 2y + y2 = 22 + 1 Combine like terms: 22 + 1 = 23 1 + 2y + y2 = 23 Factor a perfect square on the left side: (y + 1)(y + 1) = 23 Calculate the square root of the right side: 4.795831523 Break this problem into two subproblems by setting (y + 1) equal to 4.795831523 and -4.795831523.Subproblem 1
y + 1 = 4.795831523 Simplifying y + 1 = 4.795831523 Reorder the terms: 1 + y = 4.795831523 Solving 1 + y = 4.795831523 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + y = 4.795831523 + -1 Combine like terms: 1 + -1 = 0 0 + y = 4.795831523 + -1 y = 4.795831523 + -1 Combine like terms: 4.795831523 + -1 = 3.795831523 y = 3.795831523 Simplifying y = 3.795831523Subproblem 2
y + 1 = -4.795831523 Simplifying y + 1 = -4.795831523 Reorder the terms: 1 + y = -4.795831523 Solving 1 + y = -4.795831523 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + y = -4.795831523 + -1 Combine like terms: 1 + -1 = 0 0 + y = -4.795831523 + -1 y = -4.795831523 + -1 Combine like terms: -4.795831523 + -1 = -5.795831523 y = -5.795831523 Simplifying y = -5.795831523Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.795831523, -5.795831523}
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