2x^4+15=11x^2

Solution for 2x^4+15=11x^2 equation:

Simplifying
2x4 + 15 = 11x2

Reorder the terms:
15 + 2x4 = 11x2

Solving
15 + 2x4 = 11x2

Solving for variable 'x'.

Reorder the terms:
15 + -11x2 + 2x4 = 11x2 + -11x2

Combine like terms: 11x2 + -11x2 = 0
15 + -11x2 + 2x4 = 0

Factor a trinomial.
(5 + -2x2)(3 + -1x2) = 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 '(3 + -1x2)' equal to zero and attempt to solve:

Simplifying
3 + -1x2 = 0

Solving
3 + -1x2 = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x2 = 0 + -3
-1x2 = 0 + -3

Combine like terms: 0 + -3 = -3
-1x2 = -3

Divide each side by '-1'.
x2 = 3

Simplifying
x2 = 3

Take the square root of each side:
x = {-1.732050808, 1.732050808}
Solution
x = {-1.58113883, 1.58113883, -1.732050808, 1.732050808}