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Simplifying (y + 2)(y + 2) = 3 Reorder the terms: (2 + y)(y + 2) = 3 Reorder the terms: (2 + y)(2 + y) = 3 Multiply (2 + y) * (2 + y) (2(2 + y) + y(2 + y)) = 3 ((2 * 2 + y * 2) + y(2 + y)) = 3 ((4 + 2y) + y(2 + y)) = 3 (4 + 2y + (2 * y + y * y)) = 3 (4 + 2y + (2y + y2)) = 3 Combine like terms: 2y + 2y = 4y (4 + 4y + y2) = 3 Solving 4 + 4y + y2 = 3 Solving for variable 'y'. Reorder the terms: 4 + -3 + 4y + y2 = 3 + -3 Combine like terms: 4 + -3 = 1 1 + 4y + y2 = 3 + -3 Combine like terms: 3 + -3 = 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 = 3 4 + 4y + y2 = 3 Factor a perfect square on the left side: (y + 2)(y + 2) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (y + 2) equal to 1.732050808 and -1.732050808.Subproblem 1
y + 2 = 1.732050808 Simplifying y + 2 = 1.732050808 Reorder the terms: 2 + y = 1.732050808 Solving 2 + y = 1.732050808 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 = 1.732050808 + -2 Combine like terms: 2 + -2 = 0 0 + y = 1.732050808 + -2 y = 1.732050808 + -2 Combine like terms: 1.732050808 + -2 = -0.267949192 y = -0.267949192 Simplifying y = -0.267949192Subproblem 2
y + 2 = -1.732050808 Simplifying y + 2 = -1.732050808 Reorder the terms: 2 + y = -1.732050808 Solving 2 + y = -1.732050808 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 = -1.732050808 + -2 Combine like terms: 2 + -2 = 0 0 + y = -1.732050808 + -2 y = -1.732050808 + -2 Combine like terms: -1.732050808 + -2 = -3.732050808 y = -3.732050808 Simplifying y = -3.732050808Solution
The solution to the problem is based on the solutions from the subproblems. y = {-0.267949192, -3.732050808}
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