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Simplifying y4 + 2y2 + -4 = 3 Reorder the terms: -4 + 2y2 + y4 = 3 Solving -4 + 2y2 + y4 = 3 Solving for variable 'y'. Reorder the terms: -4 + -3 + 2y2 + y4 = 3 + -3 Combine like terms: -4 + -3 = -7 -7 + 2y2 + y4 = 3 + -3 Combine like terms: 3 + -3 = 0 -7 + 2y2 + y4 = 0 Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + 2y2 + 7 + y4 = 0 + 7 Reorder the terms: -7 + 7 + 2y2 + y4 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 2y2 + y4 = 0 + 7 2y2 + y4 = 0 + 7 Combine like terms: 0 + 7 = 7 2y2 + y4 = 7 The y term is 2y2. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2y2 + 1 + y4 = 7 + 1 Reorder the terms: 1 + 2y2 + y4 = 7 + 1 Combine like terms: 7 + 1 = 8 1 + 2y2 + y4 = 8 Factor a perfect square on the left side: (y2 + 1)(y2 + 1) = 8 Calculate the square root of the right side: 2.828427125 Break this problem into two subproblems by setting (y2 + 1) equal to 2.828427125 and -2.828427125.Subproblem 1
y2 + 1 = 2.828427125 Simplifying y2 + 1 = 2.828427125 Reorder the terms: 1 + y2 = 2.828427125 Solving 1 + y2 = 2.828427125 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 + y2 = 2.828427125 + -1 Combine like terms: 1 + -1 = 0 0 + y2 = 2.828427125 + -1 y2 = 2.828427125 + -1 Combine like terms: 2.828427125 + -1 = 1.828427125 y2 = 1.828427125 Simplifying y2 = 1.828427125 Take the square root of each side: y = {-1.35219345, 1.35219345}Subproblem 2
y2 + 1 = -2.828427125 Simplifying y2 + 1 = -2.828427125 Reorder the terms: 1 + y2 = -2.828427125 Solving 1 + y2 = -2.828427125 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 + y2 = -2.828427125 + -1 Combine like terms: 1 + -1 = 0 0 + y2 = -2.828427125 + -1 y2 = -2.828427125 + -1 Combine like terms: -2.828427125 + -1 = -3.828427125 y2 = -3.828427125 Simplifying y2 = -3.828427125 Reorder the terms: 3.828427125 + y2 = -3.828427125 + 3.828427125 Combine like terms: -3.828427125 + 3.828427125 = 0.000000000 3.828427125 + y2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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