8x^4+5x^2-12=0

Solution for 8x^4+5x^2-12=0 equation:

Simplifying
8x4 + 5x2 + -12 = 0

Reorder the terms:
-12 + 5x2 + 8x4 = 0

Solving
-12 + 5x2 + 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'.
-1.5 + 0.625x2 + x4 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + 0.625x2 + 1.5 + x4 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + 0.625x2 + x4 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + 0.625x2 + x4 = 0 + 1.5
0.625x2 + x4 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
0.625x2 + x4 = 1.5

The x term is 0.625x2.  Take half its coefficient (0.3125).
Square it (0.09765625) and add it to both sides.

Add '0.09765625' to each side of the equation.
0.625x2 + 0.09765625 + x4 = 1.5 + 0.09765625

Reorder the terms:
0.09765625 + 0.625x2 + x4 = 1.5 + 0.09765625

Combine like terms: 1.5 + 0.09765625 = 1.59765625
0.09765625 + 0.625x2 + x4 = 1.59765625

Factor a perfect square on the left side:
(x2 + 0.3125)(x2 + 0.3125) = 1.59765625

Calculate the square root of the right side: 1.263984276

Break this problem into two subproblems by setting 
(x2 + 0.3125) equal to 1.263984276 and -1.263984276.

Subproblem 1
x2 + 0.3125 = 1.263984276

Simplifying
x2 + 0.3125 = 1.263984276

Reorder the terms:
0.3125 + x2 = 1.263984276

Solving
0.3125 + x2 = 1.263984276

Solving for variable 'x'.

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

Add '-0.3125' to each side of the equation.
0.3125 + -0.3125 + x2 = 1.263984276 + -0.3125

Combine like terms: 0.3125 + -0.3125 = 0.0000
0.0000 + x2 = 1.263984276 + -0.3125
x2 = 1.263984276 + -0.3125

Combine like terms: 1.263984276 + -0.3125 = 0.951484276
x2 = 0.951484276

Simplifying
x2 = 0.951484276

Take the square root of each side:
x = {-0.975440555, 0.975440555}

Subproblem 2
x2 + 0.3125 = -1.263984276

Simplifying
x2 + 0.3125 = -1.263984276

Reorder the terms:
0.3125 + x2 = -1.263984276

Solving
0.3125 + x2 = -1.263984276

Solving for variable 'x'.

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

Add '-0.3125' to each side of the equation.
0.3125 + -0.3125 + x2 = -1.263984276 + -0.3125

Combine like terms: 0.3125 + -0.3125 = 0.0000
0.0000 + x2 = -1.263984276 + -0.3125
x2 = -1.263984276 + -0.3125

Combine like terms: -1.263984276 + -0.3125 = -1.576484276
x2 = -1.576484276

Simplifying
x2 = -1.576484276

Reorder the terms:
1.576484276 + x2 = -1.576484276 + 1.576484276

Combine like terms: -1.576484276 + 1.576484276 = 0.000000000
1.576484276 + 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.