x^2(x^2+1)=361

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Solution for x^2(x^2+1)=361 equation: 


Simplifying
x2(x2 + 1) = 361

Reorder the terms:
x2(1 + x2) = 361
(1 * x2 + x2 * x2) = 361
(1x2 + x4) = 361

Solving
1x2 + x4 = 361

Solving for variable 'x'.

Reorder the terms:
-361 + 1x2 + x4 = 361 + -361

Combine like terms: 361 + -361 = 0
-361 + 1x2 + x4 = 0

Begin completing the square.

Move the constant term to the right:

Add '361' to each side of the equation.
-361 + 1x2 + 361 + x4 = 0 + 361

Reorder the terms:
-361 + 361 + 1x2 + x4 = 0 + 361

Combine like terms: -361 + 361 = 0
0 + 1x2 + x4 = 0 + 361
1x2 + x4 = 0 + 361

Combine like terms: 0 + 361 = 361
1x2 + x4 = 361

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.
x2 + 0.25 + x4 = 361 + 0.25

Reorder the terms:
0.25 + x2 + x4 = 361 + 0.25

Combine like terms: 361 + 0.25 = 361.25
0.25 + x2 + x4 = 361.25

Factor a perfect square on the left side:
(x2 + 0.5)(x2 + 0.5) = 361.25

Calculate the square root of the right side: 19.006577809

Break this problem into two subproblems by setting 
(x2 + 0.5) equal to 19.006577809 and -19.006577809.


Subproblem 1
x2 + 0.5 = 19.006577809

Simplifying
x2 + 0.5 = 19.006577809

Reorder the terms:
0.5 + x2 = 19.006577809

Solving
0.5 + x2 = 19.006577809

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x2 = 19.006577809 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x2 = 19.006577809 + -0.5
x2 = 19.006577809 + -0.5

Combine like terms: 19.006577809 + -0.5 = 18.506577809
x2 = 18.506577809

Simplifying
x2 = 18.506577809

Take the square root of each side:
x = {-4.30192722, 4.30192722}


Subproblem 2
x2 + 0.5 = -19.006577809

Simplifying
x2 + 0.5 = -19.006577809

Reorder the terms:
0.5 + x2 = -19.006577809

Solving
0.5 + x2 = -19.006577809

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x2 = -19.006577809 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x2 = -19.006577809 + -0.5
x2 = -19.006577809 + -0.5

Combine like terms: -19.006577809 + -0.5 = -19.506577809
x2 = -19.506577809

Simplifying
x2 = -19.506577809

Reorder the terms:
19.506577809 + x2 = -19.506577809 + 19.506577809

Combine like terms: -19.506577809 + 19.506577809 = 0.000000000
19.506577809 + 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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