9x^4-61x^2+52=0

Solution for 9x^4-61x^2+52=0 equation:

Simplifying
9x4 + -61x2 + 52 = 0

Reorder the terms:
52 + -61x2 + 9x4 = 0

Solving
52 + -61x2 + 9x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(1 + -1x2)(52 + -9x2) = 0

Factor a difference between two squares.
((1 + x)(1 + -1x))(52 + -9x2) = 0

Subproblem 1
Set the factor '(52 + -9x2)' equal to zero and attempt to solve:

Simplifying
52 + -9x2 = 0

Solving
52 + -9x2 = 0

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

Add '-52' to each side of the equation.
52 + -52 + -9x2 = 0 + -52

Combine like terms: 52 + -52 = 0
0 + -9x2 = 0 + -52
-9x2 = 0 + -52

Combine like terms: 0 + -52 = -52
-9x2 = -52

Divide each side by '-9'.
x2 = 5.777777778

Simplifying
x2 = 5.777777778

Take the square root of each side:
x = {-2.40370085, 2.40370085}
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 = {-2.40370085, 2.40370085, -1, 1}