24b^2+25=b^4

Solution for 24b^2+25=b^4 equation:

Simplifying
24b2 + 25 = b4

Reorder the terms:
25 + 24b2 = b4

Solving
25 + 24b2 = b4

Solving for variable 'b'.

Combine like terms: b4 + -1b4 = 0
25 + 24b2 + -1b4 = 0

Factor a trinomial.
(25 + -1b2)(1 + b2) = 0

Factor a difference between two squares.
((5 + b)(5 + -1b))(1 + b2) = 0

Subproblem 1
Set the factor '(1 + b2)' equal to zero and attempt to solve:

Simplifying
1 + b2 = 0

Solving
1 + b2 = 0

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

Add '-1' to each side of the equation.
1 + -1 + b2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + b2 = 0 + -1
b2 = 0 + -1

Combine like terms: 0 + -1 = -1
b2 = -1

Simplifying
b2 = -1

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 '(5 + b)' equal to zero and attempt to solve:

Simplifying
5 + b = 0

Solving
5 + b = 0

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

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

Combine like terms: 5 + -5 = 0
0 + b = 0 + -5
b = 0 + -5

Combine like terms: 0 + -5 = -5
b = -5

Simplifying
b = -5
Subproblem 3
Set the factor '(5 + -1b)' equal to zero and attempt to solve:

Simplifying
5 + -1b = 0

Solving
5 + -1b = 0

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

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

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

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

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

Simplifying
b = 5
Solution
b = {-5, 5}