2x^4-7x^2+5=0

Solution for 2x^4-7x^2+5=0 equation:

Simplifying
2x4 + -7x2 + 5 = 0

Reorder the terms:
5 + -7x2 + 2x4 = 0

Solving
5 + -7x2 + 2x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(1 + -1x2)(5 + -2x2) = 0

Factor a difference between two squares.
((1 + x)(1 + -1x))(5 + -2x2) = 0

Subproblem 1
Set the factor '(5 + -2x2)' equal to zero and attempt to solve:

Simplifying
5 + -2x2 = 0

Solving
5 + -2x2 = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x2 = 0 + -5
-2x2 = 0 + -5

Combine like terms: 0 + -5 = -5
-2x2 = -5

Divide each side by '-2'.
x2 = 2.5

Simplifying
x2 = 2.5

Take the square root of each side:
x = {-1.58113883, 1.58113883}
Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 0

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

Add '-1' to each side of the equation.
1 + -1 + x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + x = 0 + -1
x = 0 + -1

Combine like terms: 0 + -1 = -1
x = -1

Simplifying
x = -1
Subproblem 3
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1x = 0 + -1
-1x = 0 + -1

Combine like terms: 0 + -1 = -1
-1x = -1

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Solution
x = {-1.58113883, 1.58113883, -1, 1}