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Simplifying y4 + -2y2 + -6 = 0 Reorder the terms: -6 + -2y2 + y4 = 0 Solving -6 + -2y2 + y4 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + -2y2 + 6 + y4 = 0 + 6 Reorder the terms: -6 + 6 + -2y2 + y4 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -2y2 + y4 = 0 + 6 -2y2 + y4 = 0 + 6 Combine like terms: 0 + 6 = 6 -2y2 + y4 = 6 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 = 6 + 1 Reorder the terms: 1 + -2y2 + y4 = 6 + 1 Combine like terms: 6 + 1 = 7 1 + -2y2 + y4 = 7 Factor a perfect square on the left side: (y2 + -1)(y2 + -1) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (y2 + -1) equal to 2.645751311 and -2.645751311.Subproblem 1
y2 + -1 = 2.645751311 Simplifying y2 + -1 = 2.645751311 Reorder the terms: -1 + y2 = 2.645751311 Solving -1 + y2 = 2.645751311 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 = 2.645751311 + 1 Combine like terms: -1 + 1 = 0 0 + y2 = 2.645751311 + 1 y2 = 2.645751311 + 1 Combine like terms: 2.645751311 + 1 = 3.645751311 y2 = 3.645751311 Simplifying y2 = 3.645751311 Take the square root of each side: y = {-1.909385061, 1.909385061}Subproblem 2
y2 + -1 = -2.645751311 Simplifying y2 + -1 = -2.645751311 Reorder the terms: -1 + y2 = -2.645751311 Solving -1 + y2 = -2.645751311 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 = -2.645751311 + 1 Combine like terms: -1 + 1 = 0 0 + y2 = -2.645751311 + 1 y2 = -2.645751311 + 1 Combine like terms: -2.645751311 + 1 = -1.645751311 y2 = -1.645751311 Simplifying y2 = -1.645751311 Reorder the terms: 1.645751311 + y2 = -1.645751311 + 1.645751311 Combine like terms: -1.645751311 + 1.645751311 = 0.000000000 1.645751311 + 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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