2r^4+46r^2=100

Solution for 2r^4+46r^2=100 equation:

Simplifying
2r4 + 46r2 = 100

Reorder the terms:
46r2 + 2r4 = 100

Solving
46r2 + 2r4 = 100

Solving for variable 'r'.

Reorder the terms:
-100 + 46r2 + 2r4 = 100 + -100

Combine like terms: 100 + -100 = 0
-100 + 46r2 + 2r4 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-50 + 23r2 + r4) = 0

Factor a trinomial.
2((-25 + -1r2)(2 + -1r2)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-25 + -1r2)' equal to zero and attempt to solve:

Simplifying
-25 + -1r2 = 0

Solving
-25 + -1r2 = 0

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

Add '25' to each side of the equation.
-25 + 25 + -1r2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + -1r2 = 0 + 25
-1r2 = 0 + 25

Combine like terms: 0 + 25 = 25
-1r2 = 25

Divide each side by '-1'.
r2 = -25

Simplifying
r2 = -25

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(2 + -1r2)' equal to zero and attempt to solve:

Simplifying
2 + -1r2 = 0

Solving
2 + -1r2 = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1r2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1r2 = 0 + -2
-1r2 = 0 + -2

Combine like terms: 0 + -2 = -2
-1r2 = -2

Divide each side by '-1'.
r2 = 2

Simplifying
r2 = 2

Take the square root of each side:
r = {-1.414213562, 1.414213562}
Solution
r = {-1.414213562, 1.414213562}