7x^2(7x^2+2)=54

Solution for 7x^2(7x^2+2)=54 equation:

Simplifying
7x2(7x2 + 2) = 54

Reorder the terms:
7x2(2 + 7x2) = 54
(2 * 7x2 + 7x2 * 7x2) = 54
(14x2 + 49x4) = 54

Solving
14x2 + 49x4 = 54

Solving for variable 'x'.

Reorder the terms:
-54 + 14x2 + 49x4 = 54 + -54

Combine like terms: 54 + -54 = 0
-54 + 14x2 + 49x4 = 0

Begin completing the square.  Divide all terms by
49 the coefficient of the squared term: 

Divide each side by '49'.
-1.102040816 + 0.2857142857x2 + x4 = 0

Move the constant term to the right:

Add '1.102040816' to each side of the equation.
-1.102040816 + 0.2857142857x2 + 1.102040816 + x4 = 0 + 1.102040816

Reorder the terms:
-1.102040816 + 1.102040816 + 0.2857142857x2 + x4 = 0 + 1.102040816

Combine like terms: -1.102040816 + 1.102040816 = 0.000000000
0.000000000 + 0.2857142857x2 + x4 = 0 + 1.102040816
0.2857142857x2 + x4 = 0 + 1.102040816

Combine like terms: 0 + 1.102040816 = 1.102040816
0.2857142857x2 + x4 = 1.102040816

The x term is 0.2857142857x2.  Take half its coefficient (0.1428571429).
Square it (0.02040816328) and add it to both sides.

Add '0.02040816328' to each side of the equation.
0.2857142857x2 + 0.02040816328 + x4 = 1.102040816 + 0.02040816328

Reorder the terms:
0.02040816328 + 0.2857142857x2 + x4 = 1.102040816 + 0.02040816328

Combine like terms: 1.102040816 + 0.02040816328 = 1.12244897928
0.02040816328 + 0.2857142857x2 + x4 = 1.12244897928

Factor a perfect square on the left side:
(x2 + 0.1428571429)(x2 + 0.1428571429) = 1.12244897928

Calculate the square root of the right side: 1.059456927

Break this problem into two subproblems by setting 
(x2 + 0.1428571429) equal to 1.059456927 and -1.059456927.

Subproblem 1
x2 + 0.1428571429 = 1.059456927

Simplifying
x2 + 0.1428571429 = 1.059456927

Reorder the terms:
0.1428571429 + x2 = 1.059456927

Solving
0.1428571429 + x2 = 1.059456927

Solving for variable 'x'.

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

Add '-0.1428571429' to each side of the equation.
0.1428571429 + -0.1428571429 + x2 = 1.059456927 + -0.1428571429

Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000
0.0000000000 + x2 = 1.059456927 + -0.1428571429
x2 = 1.059456927 + -0.1428571429

Combine like terms: 1.059456927 + -0.1428571429 = 0.9165997841
x2 = 0.9165997841

Simplifying
x2 = 0.9165997841

Take the square root of each side:
x = {-0.957392179, 0.957392179}

Subproblem 2
x2 + 0.1428571429 = -1.059456927

Simplifying
x2 + 0.1428571429 = -1.059456927

Reorder the terms:
0.1428571429 + x2 = -1.059456927

Solving
0.1428571429 + x2 = -1.059456927

Solving for variable 'x'.

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

Add '-0.1428571429' to each side of the equation.
0.1428571429 + -0.1428571429 + x2 = -1.059456927 + -0.1428571429

Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000
0.0000000000 + x2 = -1.059456927 + -0.1428571429
x2 = -1.059456927 + -0.1428571429

Combine like terms: -1.059456927 + -0.1428571429 = -1.2023140699
x2 = -1.2023140699

Simplifying
x2 = -1.2023140699

Reorder the terms:
1.2023140699 + x2 = -1.2023140699 + 1.2023140699

Combine like terms: -1.2023140699 + 1.2023140699 = 0.0000000000
1.2023140699 + x2 = 0.0000000000

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.