0=-4x^4+45x^2-500

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Solution for 0=-4x^4+45x^2-500 equation: 


Simplifying
0 = -4x4 + 45x2 + -500

Reorder the terms:
0 = -500 + 45x2 + -4x4

Solving
0 = -500 + 45x2 + -4x4

Solving for variable 'x'.

Combine like terms: 0 + 500 = 500
500 + -45x2 + 4x4 = -500 + 45x2 + -4x4 + 500 + -45x2 + 4x4

Reorder the terms:
500 + -45x2 + 4x4 = -500 + 500 + 45x2 + -45x2 + -4x4 + 4x4

Combine like terms: -500 + 500 = 0
500 + -45x2 + 4x4 = 0 + 45x2 + -45x2 + -4x4 + 4x4
500 + -45x2 + 4x4 = 45x2 + -45x2 + -4x4 + 4x4

Combine like terms: 45x2 + -45x2 = 0
500 + -45x2 + 4x4 = 0 + -4x4 + 4x4
500 + -45x2 + 4x4 = -4x4 + 4x4

Combine like terms: -4x4 + 4x4 = 0
500 + -45x2 + 4x4 = 0

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

Divide each side by '4'.
125 + -11.25x2 + x4 = 0

Move the constant term to the right:

Add '-125' to each side of the equation.
125 + -11.25x2 + -125 + x4 = 0 + -125

Reorder the terms:
125 + -125 + -11.25x2 + x4 = 0 + -125

Combine like terms: 125 + -125 = 0
0 + -11.25x2 + x4 = 0 + -125
-11.25x2 + x4 = 0 + -125

Combine like terms: 0 + -125 = -125
-11.25x2 + x4 = -125

The x term is -11.25x2.  Take half its coefficient (-5.625).
Square it (31.640625) and add it to both sides.

Add '31.640625' to each side of the equation.
-11.25x2 + 31.640625 + x4 = -125 + 31.640625

Reorder the terms:
31.640625 + -11.25x2 + x4 = -125 + 31.640625

Combine like terms: -125 + 31.640625 = -93.359375
31.640625 + -11.25x2 + x4 = -93.359375

Factor a perfect square on the left side:
(x2 + -5.625)(x2 + -5.625) = -93.359375

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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