r^4-7r^2=-10

Solution for r^4-7r^2=-10 equation:

Simplifying
r4 + -7r2 = -10

Reorder the terms:
-7r2 + r4 = -10

Solving
-7r2 + r4 = -10

Solving for variable 'r'.

Reorder the terms:
10 + -7r2 + r4 = -10 + 10

Combine like terms: -10 + 10 = 0
10 + -7r2 + r4 = 0

Factor a trinomial.
(2 + -1r2)(5 + -1r2) = 0

Subproblem 1
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}
Subproblem 2
Set the factor '(5 + -1r2)' equal to zero and attempt to solve:

Simplifying
5 + -1r2 = 0

Solving
5 + -1r2 = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1r2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1r2 = 0 + -5
-1r2 = 0 + -5

Combine like terms: 0 + -5 = -5
-1r2 = -5

Divide each side by '-1'.
r2 = 5

Simplifying
r2 = 5

Take the square root of each side:
r = {-2.236067978, 2.236067978}
Solution
r = {-1.414213562, 1.414213562, -2.236067978, 2.236067978}