x^2(x^2+25)=(4x^2+25)

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Solution for x^2(x^2+25)=(4x^2+25) equation: 


Simplifying
x2(x2 + 25) = (4x2 + 25)

Reorder the terms:
x2(25 + x2) = (4x2 + 25)
(25 * x2 + x2 * x2) = (4x2 + 25)
(25x2 + x4) = (4x2 + 25)

Reorder the terms:
25x2 + x4 = (25 + 4x2)

Remove parenthesis around (25 + 4x2)
25x2 + x4 = 25 + 4x2

Solving
25x2 + x4 = 25 + 4x2

Solving for variable 'x'.

Reorder the terms:
-25 + 25x2 + -4x2 + x4 = 25 + 4x2 + -25 + -4x2

Combine like terms: 25x2 + -4x2 = 21x2
-25 + 21x2 + x4 = 25 + 4x2 + -25 + -4x2

Reorder the terms:
-25 + 21x2 + x4 = 25 + -25 + 4x2 + -4x2

Combine like terms: 25 + -25 = 0
-25 + 21x2 + x4 = 0 + 4x2 + -4x2
-25 + 21x2 + x4 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-25 + 21x2 + x4 = 0

Begin completing the square.

Move the constant term to the right:

Add '25' to each side of the equation.
-25 + 21x2 + 25 + x4 = 0 + 25

Reorder the terms:
-25 + 25 + 21x2 + x4 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + 21x2 + x4 = 0 + 25
21x2 + x4 = 0 + 25

Combine like terms: 0 + 25 = 25
21x2 + x4 = 25

The x term is 21x2.  Take half its coefficient (10.5).
Square it (110.25) and add it to both sides.

Add '110.25' to each side of the equation.
21x2 + 110.25 + x4 = 25 + 110.25

Reorder the terms:
110.25 + 21x2 + x4 = 25 + 110.25

Combine like terms: 25 + 110.25 = 135.25
110.25 + 21x2 + x4 = 135.25

Factor a perfect square on the left side:
(x2 + 10.5)(x2 + 10.5) = 135.25

Calculate the square root of the right side: 11.62970335

Break this problem into two subproblems by setting 
(x2 + 10.5) equal to 11.62970335 and -11.62970335.


Subproblem 1
x2 + 10.5 = 11.62970335

Simplifying
x2 + 10.5 = 11.62970335

Reorder the terms:
10.5 + x2 = 11.62970335

Solving
10.5 + x2 = 11.62970335

Solving for variable 'x'.

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

Add '-10.5' to each side of the equation.
10.5 + -10.5 + x2 = 11.62970335 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + x2 = 11.62970335 + -10.5
x2 = 11.62970335 + -10.5

Combine like terms: 11.62970335 + -10.5 = 1.12970335
x2 = 1.12970335

Simplifying
x2 = 1.12970335

Take the square root of each side:
x = {-1.06287504, 1.06287504}


Subproblem 2
x2 + 10.5 = -11.62970335

Simplifying
x2 + 10.5 = -11.62970335

Reorder the terms:
10.5 + x2 = -11.62970335

Solving
10.5 + x2 = -11.62970335

Solving for variable 'x'.

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

Add '-10.5' to each side of the equation.
10.5 + -10.5 + x2 = -11.62970335 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + x2 = -11.62970335 + -10.5
x2 = -11.62970335 + -10.5

Combine like terms: -11.62970335 + -10.5 = -22.12970335
x2 = -22.12970335

Simplifying
x2 = -22.12970335

Reorder the terms:
22.12970335 + x2 = -22.12970335 + 22.12970335

Combine like terms: -22.12970335 + 22.12970335 = 0.00000000
22.12970335 + x2 = 0.00000000

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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