9x^4-60x^2+162=0

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Solution for 9x^4-60x^2+162=0 equation: 


Simplifying
9x4 + -60x2 + 162 = 0

Reorder the terms:
162 + -60x2 + 9x4 = 0

Solving
162 + -60x2 + 9x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(54 + -20x2 + 3x4) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(54 + -20x2 + 3x4)' equal to zero and attempt to solve:

Simplifying
54 + -20x2 + 3x4 = 0

Solving
54 + -20x2 + 3x4 = 0

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
18 + -6.666666667x2 + x4 = 0

Move the constant term to the right:

Add '-18' to each side of the equation.
18 + -6.666666667x2 + -18 + x4 = 0 + -18

Reorder the terms:
18 + -18 + -6.666666667x2 + x4 = 0 + -18

Combine like terms: 18 + -18 = 0
0 + -6.666666667x2 + x4 = 0 + -18
-6.666666667x2 + x4 = 0 + -18

Combine like terms: 0 + -18 = -18
-6.666666667x2 + x4 = -18

The x term is -6.666666667x2.  Take half its coefficient (-3.333333334).
Square it (11.11111112) and add it to both sides.

Add '11.11111112' to each side of the equation.
-6.666666667x2 + 11.11111112 + x4 = -18 + 11.11111112

Reorder the terms:
11.11111112 + -6.666666667x2 + x4 = -18 + 11.11111112

Combine like terms: -18 + 11.11111112 = -6.88888888
11.11111112 + -6.666666667x2 + x4 = -6.88888888

Factor a perfect square on the left side:
(x2 + -3.333333334)(x2 + -3.333333334) = -6.88888888

Can't calculate square root of the right side.

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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