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Simplifying (y + 1)(y + 1) + -48 = 0 Reorder the terms: (1 + y)(y + 1) + -48 = 0 Reorder the terms: (1 + y)(1 + y) + -48 = 0 Multiply (1 + y) * (1 + y) (1(1 + y) + y(1 + y)) + -48 = 0 ((1 * 1 + y * 1) + y(1 + y)) + -48 = 0 ((1 + 1y) + y(1 + y)) + -48 = 0 (1 + 1y + (1 * y + y * y)) + -48 = 0 (1 + 1y + (1y + y2)) + -48 = 0 Combine like terms: 1y + 1y = 2y (1 + 2y + y2) + -48 = 0 Reorder the terms: 1 + -48 + 2y + y2 = 0 Combine like terms: 1 + -48 = -47 -47 + 2y + y2 = 0 Solving -47 + 2y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '47' to each side of the equation. -47 + 2y + 47 + y2 = 0 + 47 Reorder the terms: -47 + 47 + 2y + y2 = 0 + 47 Combine like terms: -47 + 47 = 0 0 + 2y + y2 = 0 + 47 2y + y2 = 0 + 47 Combine like terms: 0 + 47 = 47 2y + y2 = 47 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 = 47 + 1 Reorder the terms: 1 + 2y + y2 = 47 + 1 Combine like terms: 47 + 1 = 48 1 + 2y + y2 = 48 Factor a perfect square on the left side: (y + 1)(y + 1) = 48 Calculate the square root of the right side: 6.92820323 Break this problem into two subproblems by setting (y + 1) equal to 6.92820323 and -6.92820323.Subproblem 1
y + 1 = 6.92820323 Simplifying y + 1 = 6.92820323 Reorder the terms: 1 + y = 6.92820323 Solving 1 + y = 6.92820323 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 = 6.92820323 + -1 Combine like terms: 1 + -1 = 0 0 + y = 6.92820323 + -1 y = 6.92820323 + -1 Combine like terms: 6.92820323 + -1 = 5.92820323 y = 5.92820323 Simplifying y = 5.92820323Subproblem 2
y + 1 = -6.92820323 Simplifying y + 1 = -6.92820323 Reorder the terms: 1 + y = -6.92820323 Solving 1 + y = -6.92820323 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 = -6.92820323 + -1 Combine like terms: 1 + -1 = 0 0 + y = -6.92820323 + -1 y = -6.92820323 + -1 Combine like terms: -6.92820323 + -1 = -7.92820323 y = -7.92820323 Simplifying y = -7.92820323Solution
The solution to the problem is based on the solutions from the subproblems. y = {5.92820323, -7.92820323}
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