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Simplifying (y + 1)(y + 1) = (2y + -2)(2 + -3) Reorder the terms: (1 + y)(y + 1) = (2y + -2)(2 + -3) Reorder the terms: (1 + y)(1 + y) = (2y + -2)(2 + -3) Multiply (1 + y) * (1 + y) (1(1 + y) + y(1 + y)) = (2y + -2)(2 + -3) ((1 * 1 + y * 1) + y(1 + y)) = (2y + -2)(2 + -3) ((1 + 1y) + y(1 + y)) = (2y + -2)(2 + -3) (1 + 1y + (1 * y + y * y)) = (2y + -2)(2 + -3) (1 + 1y + (1y + y2)) = (2y + -2)(2 + -3) Combine like terms: 1y + 1y = 2y (1 + 2y + y2) = (2y + -2)(2 + -3) Reorder the terms: 1 + 2y + y2 = (-2 + 2y)(2 + -3) Combine like terms: 2 + -3 = -1 1 + 2y + y2 = (-2 + 2y)(-1) Reorder the terms for easier multiplication: 1 + 2y + y2 = -1(-2 + 2y) 1 + 2y + y2 = (-2 * -1 + 2y * -1) 1 + 2y + y2 = (2 + -2y) Solving 1 + 2y + y2 = 2 + -2y Solving for variable 'y'. Reorder the terms: 1 + -2 + 2y + 2y + y2 = 2 + -2y + -2 + 2y Combine like terms: 1 + -2 = -1 -1 + 2y + 2y + y2 = 2 + -2y + -2 + 2y Combine like terms: 2y + 2y = 4y -1 + 4y + y2 = 2 + -2y + -2 + 2y Reorder the terms: -1 + 4y + y2 = 2 + -2 + -2y + 2y Combine like terms: 2 + -2 = 0 -1 + 4y + y2 = 0 + -2y + 2y -1 + 4y + y2 = -2y + 2y Combine like terms: -2y + 2y = 0 -1 + 4y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + 4y + 1 + y2 = 0 + 1 Reorder the terms: -1 + 1 + 4y + y2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 4y + y2 = 0 + 1 4y + y2 = 0 + 1 Combine like terms: 0 + 1 = 1 4y + y2 = 1 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 = 1 + 4 Reorder the terms: 4 + 4y + y2 = 1 + 4 Combine like terms: 1 + 4 = 5 4 + 4y + y2 = 5 Factor a perfect square on the left side: (y + 2)(y + 2) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (y + 2) equal to 2.236067978 and -2.236067978.Subproblem 1
y + 2 = 2.236067978 Simplifying y + 2 = 2.236067978 Reorder the terms: 2 + y = 2.236067978 Solving 2 + y = 2.236067978 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 = 2.236067978 + -2 Combine like terms: 2 + -2 = 0 0 + y = 2.236067978 + -2 y = 2.236067978 + -2 Combine like terms: 2.236067978 + -2 = 0.236067978 y = 0.236067978 Simplifying y = 0.236067978Subproblem 2
y + 2 = -2.236067978 Simplifying y + 2 = -2.236067978 Reorder the terms: 2 + y = -2.236067978 Solving 2 + y = -2.236067978 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 = -2.236067978 + -2 Combine like terms: 2 + -2 = 0 0 + y = -2.236067978 + -2 y = -2.236067978 + -2 Combine like terms: -2.236067978 + -2 = -4.236067978 y = -4.236067978 Simplifying y = -4.236067978Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.236067978, -4.236067978}
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