y^4+7y^2-18=0

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Solution for y^4+7y^2-18=0 equation: 


Simplifying
y4 + 7y2 + -18 = 0

Reorder the terms:
-18 + 7y2 + y4 = 0

Solving
-18 + 7y2 + y4 = 0

Solving for variable 'y'.

Factor a trinomial.
(-9 + -1y2)(2 + -1y2) = 0


Subproblem 1
Set the factor '(-9 + -1y2)' equal to zero and attempt to solve:

Simplifying
-9 + -1y2 = 0

Solving
-9 + -1y2 = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1y2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1y2 = 0 + 9
-1y2 = 0 + 9

Combine like terms: 0 + 9 = 9
-1y2 = 9

Divide each side by '-1'.
y2 = -9

Simplifying
y2 = -9

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(2 + -1y2)' equal to zero and attempt to solve:

Simplifying
2 + -1y2 = 0

Solving
2 + -1y2 = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1y2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1y2 = 0 + -2
-1y2 = 0 + -2

Combine like terms: 0 + -2 = -2
-1y2 = -2

Divide each side by '-1'.
y2 = 2

Simplifying
y2 = 2

Take the square root of each side:
y = {-1.414213562, 1.414213562}
Solution
y = {-1.414213562, 1.414213562}

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