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Simplifying (y + 2)(y + 2) + -48 = 0 Reorder the terms: (2 + y)(y + 2) + -48 = 0 Reorder the terms: (2 + y)(2 + y) + -48 = 0 Multiply (2 + y) * (2 + y) (2(2 + y) + y(2 + y)) + -48 = 0 ((2 * 2 + y * 2) + y(2 + y)) + -48 = 0 ((4 + 2y) + y(2 + y)) + -48 = 0 (4 + 2y + (2 * y + y * y)) + -48 = 0 (4 + 2y + (2y + y2)) + -48 = 0 Combine like terms: 2y + 2y = 4y (4 + 4y + y2) + -48 = 0 Reorder the terms: 4 + -48 + 4y + y2 = 0 Combine like terms: 4 + -48 = -44 -44 + 4y + y2 = 0 Solving -44 + 4y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '44' to each side of the equation. -44 + 4y + 44 + y2 = 0 + 44 Reorder the terms: -44 + 44 + 4y + y2 = 0 + 44 Combine like terms: -44 + 44 = 0 0 + 4y + y2 = 0 + 44 4y + y2 = 0 + 44 Combine like terms: 0 + 44 = 44 4y + y2 = 44 The y term is 4y. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4y + 4 + y2 = 44 + 4 Reorder the terms: 4 + 4y + y2 = 44 + 4 Combine like terms: 44 + 4 = 48 4 + 4y + y2 = 48 Factor a perfect square on the left side: (y + 2)(y + 2) = 48 Calculate the square root of the right side: 6.92820323 Break this problem into two subproblems by setting (y + 2) equal to 6.92820323 and -6.92820323.Subproblem 1
y + 2 = 6.92820323 Simplifying y + 2 = 6.92820323 Reorder the terms: 2 + y = 6.92820323 Solving 2 + y = 6.92820323 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + y = 6.92820323 + -2 Combine like terms: 2 + -2 = 0 0 + y = 6.92820323 + -2 y = 6.92820323 + -2 Combine like terms: 6.92820323 + -2 = 4.92820323 y = 4.92820323 Simplifying y = 4.92820323Subproblem 2
y + 2 = -6.92820323 Simplifying y + 2 = -6.92820323 Reorder the terms: 2 + y = -6.92820323 Solving 2 + y = -6.92820323 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + y = -6.92820323 + -2 Combine like terms: 2 + -2 = 0 0 + y = -6.92820323 + -2 y = -6.92820323 + -2 Combine like terms: -6.92820323 + -2 = -8.92820323 y = -8.92820323 Simplifying y = -8.92820323Solution
The solution to the problem is based on the solutions from the subproblems. y = {4.92820323, -8.92820323}
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