7x^4-33x^2+26=0

Solution for 7x^4-33x^2+26=0 equation:

Simplifying
7x4 + -33x2 + 26 = 0

Reorder the terms:
26 + -33x2 + 7x4 = 0

Solving
26 + -33x2 + 7x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(1 + -1x2)(26 + -7x2) = 0

Factor a difference between two squares.
((1 + x)(1 + -1x))(26 + -7x2) = 0

Subproblem 1
Set the factor '(26 + -7x2)' equal to zero and attempt to solve:

Simplifying
26 + -7x2 = 0

Solving
26 + -7x2 = 0

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

Add '-26' to each side of the equation.
26 + -26 + -7x2 = 0 + -26

Combine like terms: 26 + -26 = 0
0 + -7x2 = 0 + -26
-7x2 = 0 + -26

Combine like terms: 0 + -26 = -26
-7x2 = -26

Divide each side by '-7'.
x2 = 3.714285714

Simplifying
x2 = 3.714285714

Take the square root of each side:
x = {-1.927248223, 1.927248223}
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 = {-1.927248223, 1.927248223, -1, 1}