y^4+3y^2-1=0

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Solution for y^4+3y^2-1=0 equation:


Simplifying
y4 + 3y2 + -1 = 0

Reorder the terms:
-1 + 3y2 + y4 = 0

Solving
-1 + 3y2 + y4 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 3y2 + 1 + y4 = 0 + 1

Reorder the terms:
-1 + 1 + 3y2 + y4 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 3y2 + y4 = 0 + 1
3y2 + y4 = 0 + 1

Combine like terms: 0 + 1 = 1
3y2 + y4 = 1

The y term is 3y2.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3y2 + 2.25 + y4 = 1 + 2.25

Reorder the terms:
2.25 + 3y2 + y4 = 1 + 2.25

Combine like terms: 1 + 2.25 = 3.25
2.25 + 3y2 + y4 = 3.25

Factor a perfect square on the left side:
(y2 + 1.5)(y2 + 1.5) = 3.25

Calculate the square root of the right side: 1.802775638

Break this problem into two subproblems by setting 
(y2 + 1.5) equal to 1.802775638 and -1.802775638.

Subproblem 1

y2 + 1.5 = 1.802775638 Simplifying y2 + 1.5 = 1.802775638 Reorder the terms: 1.5 + y2 = 1.802775638 Solving 1.5 + y2 = 1.802775638 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + y2 = 1.802775638 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + y2 = 1.802775638 + -1.5 y2 = 1.802775638 + -1.5 Combine like terms: 1.802775638 + -1.5 = 0.302775638 y2 = 0.302775638 Simplifying y2 = 0.302775638 Take the square root of each side: y = {-0.550250523, 0.550250523}

Subproblem 2

y2 + 1.5 = -1.802775638 Simplifying y2 + 1.5 = -1.802775638 Reorder the terms: 1.5 + y2 = -1.802775638 Solving 1.5 + y2 = -1.802775638 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + y2 = -1.802775638 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + y2 = -1.802775638 + -1.5 y2 = -1.802775638 + -1.5 Combine like terms: -1.802775638 + -1.5 = -3.302775638 y2 = -3.302775638 Simplifying y2 = -3.302775638 Reorder the terms: 3.302775638 + y2 = -3.302775638 + 3.302775638 Combine like terms: -3.302775638 + 3.302775638 = 0.000000000 3.302775638 + 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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