-x^4=4x^2+45

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


Simplifying
-1x4 = 4x2 + 45

Reorder the terms:
-1x4 = 45 + 4x2

Solving
-1x4 = 45 + 4x2

Solving for variable 'x'.

Reorder the terms:
-45 + -4x2 + -1x4 = 45 + 4x2 + -45 + -4x2

Reorder the terms:
-45 + -4x2 + -1x4 = 45 + -45 + 4x2 + -4x2

Combine like terms: 45 + -45 = 0
-45 + -4x2 + -1x4 = 0 + 4x2 + -4x2
-45 + -4x2 + -1x4 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-45 + -4x2 + -1x4 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(45 + 4x2 + x4) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(45 + 4x2 + x4)' equal to zero and attempt to solve:

Simplifying
45 + 4x2 + x4 = 0

Solving
45 + 4x2 + x4 = 0

Begin completing the square.

Move the constant term to the right:

Add '-45' to each side of the equation.
45 + 4x2 + -45 + x4 = 0 + -45

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

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

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

The x term is 4x2.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x2 + 4 + x4 = -45 + 4

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

Combine like terms: -45 + 4 = -41
4 + 4x2 + x4 = -41

Factor a perfect square on the left side:
(x2 + 2)(x2 + 2) = -41

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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