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Simplifying y2 + 2y + -36 = 0 Reorder the terms: -36 + 2y + y2 = 0 Solving -36 + 2y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + 2y + 36 + y2 = 0 + 36 Reorder the terms: -36 + 36 + 2y + y2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + 2y + y2 = 0 + 36 2y + y2 = 0 + 36 Combine like terms: 0 + 36 = 36 2y + y2 = 36 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 = 36 + 1 Reorder the terms: 1 + 2y + y2 = 36 + 1 Combine like terms: 36 + 1 = 37 1 + 2y + y2 = 37 Factor a perfect square on the left side: (y + 1)(y + 1) = 37 Calculate the square root of the right side: 6.08276253 Break this problem into two subproblems by setting (y + 1) equal to 6.08276253 and -6.08276253.Subproblem 1
y + 1 = 6.08276253 Simplifying y + 1 = 6.08276253 Reorder the terms: 1 + y = 6.08276253 Solving 1 + y = 6.08276253 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 = 6.08276253 + -1 Combine like terms: 1 + -1 = 0 0 + y = 6.08276253 + -1 y = 6.08276253 + -1 Combine like terms: 6.08276253 + -1 = 5.08276253 y = 5.08276253 Simplifying y = 5.08276253Subproblem 2
y + 1 = -6.08276253 Simplifying y + 1 = -6.08276253 Reorder the terms: 1 + y = -6.08276253 Solving 1 + y = -6.08276253 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 = -6.08276253 + -1 Combine like terms: 1 + -1 = 0 0 + y = -6.08276253 + -1 y = -6.08276253 + -1 Combine like terms: -6.08276253 + -1 = -7.08276253 y = -7.08276253 Simplifying y = -7.08276253Solution
The solution to the problem is based on the solutions from the subproblems. y = {5.08276253, -7.08276253}
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