8x^4-11x^2+1=0

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Solution for 8x^4-11x^2+1=0 equation: 


Simplifying
8x4 + -11x2 + 1 = 0

Reorder the terms:
1 + -11x2 + 8x4 = 0

Solving
1 + -11x2 + 8x4 = 0

Solving for variable 'x'.

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

Divide each side by '8'.
0.125 + -1.375x2 + x4 = 0

Move the constant term to the right:

Add '-0.125' to each side of the equation.
0.125 + -1.375x2 + -0.125 + x4 = 0 + -0.125

Reorder the terms:
0.125 + -0.125 + -1.375x2 + x4 = 0 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + -1.375x2 + x4 = 0 + -0.125
-1.375x2 + x4 = 0 + -0.125

Combine like terms: 0 + -0.125 = -0.125
-1.375x2 + x4 = -0.125

The x term is -1.375x2.  Take half its coefficient (-0.6875).
Square it (0.47265625) and add it to both sides.

Add '0.47265625' to each side of the equation.
-1.375x2 + 0.47265625 + x4 = -0.125 + 0.47265625

Reorder the terms:
0.47265625 + -1.375x2 + x4 = -0.125 + 0.47265625

Combine like terms: -0.125 + 0.47265625 = 0.34765625
0.47265625 + -1.375x2 + x4 = 0.34765625

Factor a perfect square on the left side:
(x2 + -0.6875)(x2 + -0.6875) = 0.34765625

Calculate the square root of the right side: 0.589623821

Break this problem into two subproblems by setting 
(x2 + -0.6875) equal to 0.589623821 and -0.589623821.


Subproblem 1
x2 + -0.6875 = 0.589623821

Simplifying
x2 + -0.6875 = 0.589623821

Reorder the terms:
-0.6875 + x2 = 0.589623821

Solving
-0.6875 + x2 = 0.589623821

Solving for variable 'x'.

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

Add '0.6875' to each side of the equation.
-0.6875 + 0.6875 + x2 = 0.589623821 + 0.6875

Combine like terms: -0.6875 + 0.6875 = 0.0000
0.0000 + x2 = 0.589623821 + 0.6875
x2 = 0.589623821 + 0.6875

Combine like terms: 0.589623821 + 0.6875 = 1.277123821
x2 = 1.277123821

Simplifying
x2 = 1.277123821

Take the square root of each side:
x = {-1.130099032, 1.130099032}


Subproblem 2
x2 + -0.6875 = -0.589623821

Simplifying
x2 + -0.6875 = -0.589623821

Reorder the terms:
-0.6875 + x2 = -0.589623821

Solving
-0.6875 + x2 = -0.589623821

Solving for variable 'x'.

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

Add '0.6875' to each side of the equation.
-0.6875 + 0.6875 + x2 = -0.589623821 + 0.6875

Combine like terms: -0.6875 + 0.6875 = 0.0000
0.0000 + x2 = -0.589623821 + 0.6875
x2 = -0.589623821 + 0.6875

Combine like terms: -0.589623821 + 0.6875 = 0.097876179
x2 = 0.097876179

Simplifying
x2 = 0.097876179

Take the square root of each side:
x = {-0.312851689, 0.312851689}


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.130099032, 1.130099032, -0.312851689, 0.312851689}

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