25q^2+10q+1=0

Solution for 25q^2+10q+1=0 equation:

Simplifying
25q2 + 10q + 1 = 0

Reorder the terms:
1 + 10q + 25q2 = 0

Solving
1 + 10q + 25q2 = 0

Solving for variable 'q'.

Factor a trinomial.
(1 + 5q)(1 + 5q) = 0

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

Simplifying
1 + 5q = 0

Solving
1 + 5q = 0

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

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

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

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

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

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

Simplifying
1 + 5q = 0

Solving
1 + 5q = 0

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

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

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

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

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

Simplifying
q = -0.2
Solution
q = {-0.2, -0.2}