2x^4-9x^2=90

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Solution for 2x^4-9x^2=90 equation: 


Simplifying
2x4 + -9x2 = 90

Reorder the terms:
-9x2 + 2x4 = 90

Solving
-9x2 + 2x4 = 90

Solving for variable 'x'.

Reorder the terms:
-90 + -9x2 + 2x4 = 90 + -90

Combine like terms: 90 + -90 = 0
-90 + -9x2 + 2x4 = 0

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

Divide each side by '2'.
-45 + -4.5x2 + x4 = 0

Move the constant term to the right:

Add '45' to each side of the equation.
-45 + -4.5x2 + 45 + x4 = 0 + 45

Reorder the terms:
-45 + 45 + -4.5x2 + x4 = 0 + 45

Combine like terms: -45 + 45 = 0
0 + -4.5x2 + x4 = 0 + 45
-4.5x2 + x4 = 0 + 45

Combine like terms: 0 + 45 = 45
-4.5x2 + x4 = 45

The x term is -4.5x2.  Take half its coefficient (-2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
-4.5x2 + 5.0625 + x4 = 45 + 5.0625

Reorder the terms:
5.0625 + -4.5x2 + x4 = 45 + 5.0625

Combine like terms: 45 + 5.0625 = 50.0625
5.0625 + -4.5x2 + x4 = 50.0625

Factor a perfect square on the left side:
(x2 + -2.25)(x2 + -2.25) = 50.0625

Calculate the square root of the right side: 7.075485849

Break this problem into two subproblems by setting 
(x2 + -2.25) equal to 7.075485849 and -7.075485849.


Subproblem 1
x2 + -2.25 = 7.075485849

Simplifying
x2 + -2.25 = 7.075485849

Reorder the terms:
-2.25 + x2 = 7.075485849

Solving
-2.25 + x2 = 7.075485849

Solving for variable 'x'.

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

Add '2.25' to each side of the equation.
-2.25 + 2.25 + x2 = 7.075485849 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + x2 = 7.075485849 + 2.25
x2 = 7.075485849 + 2.25

Combine like terms: 7.075485849 + 2.25 = 9.325485849
x2 = 9.325485849

Simplifying
x2 = 9.325485849

Take the square root of each side:
x = {-3.053765847, 3.053765847}


Subproblem 2
x2 + -2.25 = -7.075485849

Simplifying
x2 + -2.25 = -7.075485849

Reorder the terms:
-2.25 + x2 = -7.075485849

Solving
-2.25 + x2 = -7.075485849

Solving for variable 'x'.

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

Add '2.25' to each side of the equation.
-2.25 + 2.25 + x2 = -7.075485849 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + x2 = -7.075485849 + 2.25
x2 = -7.075485849 + 2.25

Combine like terms: -7.075485849 + 2.25 = -4.825485849
x2 = -4.825485849

Simplifying
x2 = -4.825485849

Reorder the terms:
4.825485849 + x2 = -4.825485849 + 4.825485849

Combine like terms: -4.825485849 + 4.825485849 = 0.000000000
4.825485849 + x2 = 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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