y^4+15y^2=225

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Solution for y^4+15y^2=225 equation: 


Simplifying
y4 + 15y2 = 225

Reorder the terms:
15y2 + y4 = 225

Solving
15y2 + y4 = 225

Solving for variable 'y'.

Reorder the terms:
-225 + 15y2 + y4 = 225 + -225

Combine like terms: 225 + -225 = 0
-225 + 15y2 + y4 = 0

Begin completing the square.

Move the constant term to the right:

Add '225' to each side of the equation.
-225 + 15y2 + 225 + y4 = 0 + 225

Reorder the terms:
-225 + 225 + 15y2 + y4 = 0 + 225

Combine like terms: -225 + 225 = 0
0 + 15y2 + y4 = 0 + 225
15y2 + y4 = 0 + 225

Combine like terms: 0 + 225 = 225
15y2 + y4 = 225

The y term is 15y2.  Take half its coefficient (7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
15y2 + 56.25 + y4 = 225 + 56.25

Reorder the terms:
56.25 + 15y2 + y4 = 225 + 56.25

Combine like terms: 225 + 56.25 = 281.25
56.25 + 15y2 + y4 = 281.25

Factor a perfect square on the left side:
(y2 + 7.5)(y2 + 7.5) = 281.25

Calculate the square root of the right side: 16.770509831

Break this problem into two subproblems by setting 
(y2 + 7.5) equal to 16.770509831 and -16.770509831.


Subproblem 1
y2 + 7.5 = 16.770509831

Simplifying
y2 + 7.5 = 16.770509831

Reorder the terms:
7.5 + y2 = 16.770509831

Solving
7.5 + y2 = 16.770509831

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '-7.5' to each side of the equation.
7.5 + -7.5 + y2 = 16.770509831 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + y2 = 16.770509831 + -7.5
y2 = 16.770509831 + -7.5

Combine like terms: 16.770509831 + -7.5 = 9.270509831
y2 = 9.270509831

Simplifying
y2 = 9.270509831

Take the square root of each side:
y = {-3.044751194, 3.044751194}


Subproblem 2
y2 + 7.5 = -16.770509831

Simplifying
y2 + 7.5 = -16.770509831

Reorder the terms:
7.5 + y2 = -16.770509831

Solving
7.5 + y2 = -16.770509831

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '-7.5' to each side of the equation.
7.5 + -7.5 + y2 = -16.770509831 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + y2 = -16.770509831 + -7.5
y2 = -16.770509831 + -7.5

Combine like terms: -16.770509831 + -7.5 = -24.270509831
y2 = -24.270509831

Simplifying
y2 = -24.270509831

Reorder the terms:
24.270509831 + y2 = -24.270509831 + 24.270509831

Combine like terms: -24.270509831 + 24.270509831 = 0.000000000
24.270509831 + 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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