3x^2=-x^4+4x^2-5

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Solution for 3x^2=-x^4+4x^2-5 equation:


Simplifying
3x2 = -1x4 + 4x2 + -5

Reorder the terms:
3x2 = -5 + 4x2 + -1x4

Solving
3x2 = -5 + 4x2 + -1x4

Solving for variable 'x'.

Reorder the terms:
5 + 3x2 + -4x2 + x4 = -5 + 4x2 + -1x4 + 5 + -4x2 + x4

Combine like terms: 3x2 + -4x2 = -1x2
5 + -1x2 + x4 = -5 + 4x2 + -1x4 + 5 + -4x2 + x4

Reorder the terms:
5 + -1x2 + x4 = -5 + 5 + 4x2 + -4x2 + -1x4 + x4

Combine like terms: -5 + 5 = 0
5 + -1x2 + x4 = 0 + 4x2 + -4x2 + -1x4 + x4
5 + -1x2 + x4 = 4x2 + -4x2 + -1x4 + x4

Combine like terms: 4x2 + -4x2 = 0
5 + -1x2 + x4 = 0 + -1x4 + x4
5 + -1x2 + x4 = -1x4 + x4

Combine like terms: -1x4 + x4 = 0
5 + -1x2 + x4 = 0

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + -1x2 + -5 + x4 = 0 + -5

Reorder the terms:
5 + -5 + -1x2 + x4 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x2 + x4 = 0 + -5
-1x2 + x4 = 0 + -5

Combine like terms: 0 + -5 = -5
-1x2 + x4 = -5

The x term is -1x2.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x2 + 0.25 + x4 = -5 + 0.25

Reorder the terms:
0.25 + -1x2 + x4 = -5 + 0.25

Combine like terms: -5 + 0.25 = -4.75
0.25 + -1x2 + x4 = -4.75

Factor a perfect square on the left side:
(x2 + -0.5)(x2 + -0.5) = -4.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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