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Simplifying y4 + y2 + -22 = 0 Reorder the terms: -22 + y2 + y4 = 0 Solving -22 + y2 + y4 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '22' to each side of the equation. -22 + y2 + 22 + y4 = 0 + 22 Reorder the terms: -22 + 22 + y2 + y4 = 0 + 22 Combine like terms: -22 + 22 = 0 0 + y2 + y4 = 0 + 22 y2 + y4 = 0 + 22 Combine like terms: 0 + 22 = 22 y2 + y4 = 22 The y term is y2. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. y2 + 0.25 + y4 = 22 + 0.25 Reorder the terms: 0.25 + y2 + y4 = 22 + 0.25 Combine like terms: 22 + 0.25 = 22.25 0.25 + y2 + y4 = 22.25 Factor a perfect square on the left side: (y2 + 0.5)(y2 + 0.5) = 22.25 Calculate the square root of the right side: 4.716990566 Break this problem into two subproblems by setting (y2 + 0.5) equal to 4.716990566 and -4.716990566.Subproblem 1
y2 + 0.5 = 4.716990566 Simplifying y2 + 0.5 = 4.716990566 Reorder the terms: 0.5 + y2 = 4.716990566 Solving 0.5 + y2 = 4.716990566 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + y2 = 4.716990566 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y2 = 4.716990566 + -0.5 y2 = 4.716990566 + -0.5 Combine like terms: 4.716990566 + -0.5 = 4.216990566 y2 = 4.216990566 Simplifying y2 = 4.216990566 Take the square root of each side: y = {-2.053531243, 2.053531243}Subproblem 2
y2 + 0.5 = -4.716990566 Simplifying y2 + 0.5 = -4.716990566 Reorder the terms: 0.5 + y2 = -4.716990566 Solving 0.5 + y2 = -4.716990566 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + y2 = -4.716990566 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y2 = -4.716990566 + -0.5 y2 = -4.716990566 + -0.5 Combine like terms: -4.716990566 + -0.5 = -5.216990566 y2 = -5.216990566 Simplifying y2 = -5.216990566 Reorder the terms: 5.216990566 + y2 = -5.216990566 + 5.216990566 Combine like terms: -5.216990566 + 5.216990566 = 0.000000000 5.216990566 + 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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