6y^2+y^4=3

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Solution for 6y^2+y^4=3 equation:


Simplifying
6y2 + y4 = 3

Solving
6y2 + y4 = 3

Solving for variable 'y'.

Reorder the terms:
-3 + 6y2 + y4 = 3 + -3

Combine like terms: 3 + -3 = 0
-3 + 6y2 + y4 = 0

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 6y2 + 3 + y4 = 0 + 3

Reorder the terms:
-3 + 3 + 6y2 + y4 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 6y2 + y4 = 0 + 3
6y2 + y4 = 0 + 3

Combine like terms: 0 + 3 = 3
6y2 + y4 = 3

The y term is 6y2.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6y2 + 9 + y4 = 3 + 9

Reorder the terms:
9 + 6y2 + y4 = 3 + 9

Combine like terms: 3 + 9 = 12
9 + 6y2 + y4 = 12

Factor a perfect square on the left side:
(y2 + 3)(y2 + 3) = 12

Calculate the square root of the right side: 3.464101615

Break this problem into two subproblems by setting 
(y2 + 3) equal to 3.464101615 and -3.464101615.

Subproblem 1

y2 + 3 = 3.464101615 Simplifying y2 + 3 = 3.464101615 Reorder the terms: 3 + y2 = 3.464101615 Solving 3 + y2 = 3.464101615 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + y2 = 3.464101615 + -3 Combine like terms: 3 + -3 = 0 0 + y2 = 3.464101615 + -3 y2 = 3.464101615 + -3 Combine like terms: 3.464101615 + -3 = 0.464101615 y2 = 0.464101615 Simplifying y2 = 0.464101615 Take the square root of each side: y = {-0.681250039, 0.681250039}

Subproblem 2

y2 + 3 = -3.464101615 Simplifying y2 + 3 = -3.464101615 Reorder the terms: 3 + y2 = -3.464101615 Solving 3 + y2 = -3.464101615 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + y2 = -3.464101615 + -3 Combine like terms: 3 + -3 = 0 0 + y2 = -3.464101615 + -3 y2 = -3.464101615 + -3 Combine like terms: -3.464101615 + -3 = -6.464101615 y2 = -6.464101615 Simplifying y2 = -6.464101615 Reorder the terms: 6.464101615 + y2 = -6.464101615 + 6.464101615 Combine like terms: -6.464101615 + 6.464101615 = 0.000000000 6.464101615 + 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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