x^4+9x^2+16=

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Solution for x^4+9x^2+16= equation: 


Simplifying
x4 + 9x2 + 16 = 0

Reorder the terms:
16 + 9x2 + x4 = 0

Solving
16 + 9x2 + x4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-16' to each side of the equation.
16 + 9x2 + -16 + x4 = 0 + -16

Reorder the terms:
16 + -16 + 9x2 + x4 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + 9x2 + x4 = 0 + -16
9x2 + x4 = 0 + -16

Combine like terms: 0 + -16 = -16
9x2 + x4 = -16

The x term is 9x2.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9x2 + 20.25 + x4 = -16 + 20.25

Reorder the terms:
20.25 + 9x2 + x4 = -16 + 20.25

Combine like terms: -16 + 20.25 = 4.25
20.25 + 9x2 + x4 = 4.25

Factor a perfect square on the left side:
(x2 + 4.5)(x2 + 4.5) = 4.25

Calculate the square root of the right side: 2.061552813

Break this problem into two subproblems by setting 
(x2 + 4.5) equal to 2.061552813 and -2.061552813.


Subproblem 1
x2 + 4.5 = 2.061552813

Simplifying
x2 + 4.5 = 2.061552813

Reorder the terms:
4.5 + x2 = 2.061552813

Solving
4.5 + x2 = 2.061552813

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x2 = 2.061552813 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x2 = 2.061552813 + -4.5
x2 = 2.061552813 + -4.5

Combine like terms: 2.061552813 + -4.5 = -2.438447187
x2 = -2.438447187

Simplifying
x2 = -2.438447187

Reorder the terms:
2.438447187 + x2 = -2.438447187 + 2.438447187

Combine like terms: -2.438447187 + 2.438447187 = 0.000000000
2.438447187 + x2 = 0.000000000

The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.


Subproblem 2
x2 + 4.5 = -2.061552813

Simplifying
x2 + 4.5 = -2.061552813

Reorder the terms:
4.5 + x2 = -2.061552813

Solving
4.5 + x2 = -2.061552813

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x2 = -2.061552813 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x2 = -2.061552813 + -4.5
x2 = -2.061552813 + -4.5

Combine like terms: -2.061552813 + -4.5 = -6.561552813
x2 = -6.561552813

Simplifying
x2 = -6.561552813

Reorder the terms:
6.561552813 + x2 = -6.561552813 + 6.561552813

Combine like terms: -6.561552813 + 6.561552813 = 0.000000000
6.561552813 + 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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