4x^4+3x^2-5=0

Solution for 4x^4+3x^2-5=0 equation:

Simplifying
4x4 + 3x2 + -5 = 0

Reorder the terms:
-5 + 3x2 + 4x4 = 0

Solving
-5 + 3x2 + 4x4 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
-1.25 + 0.75x2 + x4 = 0

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + 0.75x2 + 1.25 + x4 = 0 + 1.25

Reorder the terms:
-1.25 + 1.25 + 0.75x2 + x4 = 0 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + 0.75x2 + x4 = 0 + 1.25
0.75x2 + x4 = 0 + 1.25

Combine like terms: 0 + 1.25 = 1.25
0.75x2 + x4 = 1.25

The x term is 0.75x2.  Take half its coefficient (0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
0.75x2 + 0.140625 + x4 = 1.25 + 0.140625

Reorder the terms:
0.140625 + 0.75x2 + x4 = 1.25 + 0.140625

Combine like terms: 1.25 + 0.140625 = 1.390625
0.140625 + 0.75x2 + x4 = 1.390625

Factor a perfect square on the left side:
(x2 + 0.375)(x2 + 0.375) = 1.390625

Calculate the square root of the right side: 1.179247642

Break this problem into two subproblems by setting 
(x2 + 0.375) equal to 1.179247642 and -1.179247642.

Subproblem 1
x2 + 0.375 = 1.179247642

Simplifying
x2 + 0.375 = 1.179247642

Reorder the terms:
0.375 + x2 = 1.179247642

Solving
0.375 + x2 = 1.179247642

Solving for variable 'x'.

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

Add '-0.375' to each side of the equation.
0.375 + -0.375 + x2 = 1.179247642 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + x2 = 1.179247642 + -0.375
x2 = 1.179247642 + -0.375

Combine like terms: 1.179247642 + -0.375 = 0.804247642
x2 = 0.804247642

Simplifying
x2 = 0.804247642

Take the square root of each side:
x = {-0.896798552, 0.896798552}

Subproblem 2
x2 + 0.375 = -1.179247642

Simplifying
x2 + 0.375 = -1.179247642

Reorder the terms:
0.375 + x2 = -1.179247642

Solving
0.375 + x2 = -1.179247642

Solving for variable 'x'.

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

Add '-0.375' to each side of the equation.
0.375 + -0.375 + x2 = -1.179247642 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + x2 = -1.179247642 + -0.375
x2 = -1.179247642 + -0.375

Combine like terms: -1.179247642 + -0.375 = -1.554247642
x2 = -1.554247642

Simplifying
x2 = -1.554247642

Reorder the terms:
1.554247642 + x2 = -1.554247642 + 1.554247642

Combine like terms: -1.554247642 + 1.554247642 = 0.000000000
1.554247642 + 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.