y^4-12y^2+9=0

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Solution for y^4-12y^2+9=0 equation:


Simplifying
y4 + -12y2 + 9 = 0

Reorder the terms:
9 + -12y2 + y4 = 0

Solving
9 + -12y2 + y4 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-9' to each side of the equation.
9 + -12y2 + -9 + y4 = 0 + -9

Reorder the terms:
9 + -9 + -12y2 + y4 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -12y2 + y4 = 0 + -9
-12y2 + y4 = 0 + -9

Combine like terms: 0 + -9 = -9
-12y2 + y4 = -9

The y term is -12y2.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12y2 + 36 + y4 = -9 + 36

Reorder the terms:
36 + -12y2 + y4 = -9 + 36

Combine like terms: -9 + 36 = 27
36 + -12y2 + y4 = 27

Factor a perfect square on the left side:
(y2 + -6)(y2 + -6) = 27

Calculate the square root of the right side: 5.196152423

Break this problem into two subproblems by setting 
(y2 + -6) equal to 5.196152423 and -5.196152423.

Subproblem 1

y2 + -6 = 5.196152423 Simplifying y2 + -6 = 5.196152423 Reorder the terms: -6 + y2 = 5.196152423 Solving -6 + y2 = 5.196152423 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + y2 = 5.196152423 + 6 Combine like terms: -6 + 6 = 0 0 + y2 = 5.196152423 + 6 y2 = 5.196152423 + 6 Combine like terms: 5.196152423 + 6 = 11.196152423 y2 = 11.196152423 Simplifying y2 = 11.196152423 Take the square root of each side: y = {-3.346065215, 3.346065215}

Subproblem 2

y2 + -6 = -5.196152423 Simplifying y2 + -6 = -5.196152423 Reorder the terms: -6 + y2 = -5.196152423 Solving -6 + y2 = -5.196152423 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + y2 = -5.196152423 + 6 Combine like terms: -6 + 6 = 0 0 + y2 = -5.196152423 + 6 y2 = -5.196152423 + 6 Combine like terms: -5.196152423 + 6 = 0.803847577 y2 = 0.803847577 Simplifying y2 = 0.803847577 Take the square root of each side: y = {-0.896575472, 0.896575472}

Solution

The solution to the problem is based on the solutions from the subproblems. y = {-3.346065215, 3.346065215, -0.896575472, 0.896575472}

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