100e^4-629e^2+25=

Solution for 100e^4-629e^2+25= equation:

Simplifying
100e4 + -629e2 + 25 = 0

Reorder the terms:
25 + -629e2 + 100e4 = 0

Solving
25 + -629e2 + 100e4 = 0

Solving for variable 'e'.

Factor a trinomial.
(1 + -25e2)(25 + -4e2) = 0

Factor a difference between two squares.
((1 + 5e)(1 + -5e))(25 + -4e2) = 0

Factor a difference between two squares.
((5 + 2e)(5 + -2e))(1 + 5e)(1 + -5e) = 0

Subproblem 1
Set the factor '(1 + 5e)' equal to zero and attempt to solve:

Simplifying
1 + 5e = 0

Solving
1 + 5e = 0

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

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

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

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

Divide each side by '5'.
e = -0.2

Simplifying
e = -0.2
Subproblem 2
Set the factor '(1 + -5e)' equal to zero and attempt to solve:

Simplifying
1 + -5e = 0

Solving
1 + -5e = 0

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

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

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

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

Divide each side by '-5'.
e = 0.2

Simplifying
e = 0.2
Subproblem 3
Set the factor '(5 + 2e)' equal to zero and attempt to solve:

Simplifying
5 + 2e = 0

Solving
5 + 2e = 0

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

Add '-5' to each side of the equation.
5 + -5 + 2e = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2e = 0 + -5
2e = 0 + -5

Combine like terms: 0 + -5 = -5
2e = -5

Divide each side by '2'.
e = -2.5

Simplifying
e = -2.5
Subproblem 4
Set the factor '(5 + -2e)' equal to zero and attempt to solve:

Simplifying
5 + -2e = 0

Solving
5 + -2e = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2e = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2e = 0 + -5
-2e = 0 + -5

Combine like terms: 0 + -5 = -5
-2e = -5

Divide each side by '-2'.
e = 2.5

Simplifying
e = 2.5
Solution
e = {-0.2, 0.2, -2.5, 2.5}