49r^2s^2+14rs+1=

Solution for 49r^2s^2+14rs+1= equation:

Simplifying
49r2s2 + 14rs + 1 = 0

Reorder the terms:
1 + 14rs + 49r2s2 = 0

Solving
1 + 14rs + 49r2s2 = 0

Solving for variable 'r'.

Factor a trinomial.
(1 + 7rs)(1 + 7rs) = 0

Subproblem 1
Set the factor '(1 + 7rs)' equal to zero and attempt to solve:

Simplifying
1 + 7rs = 0

Solving
1 + 7rs = 0

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

Add '-1' to each side of the equation.
1 + -1 + 7rs = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 7rs = 0 + -1
7rs = 0 + -1

Combine like terms: 0 + -1 = -1
7rs = -1

Divide each side by '7s'.
r = -0.1428571429s-1

Simplifying
r = -0.1428571429s-1
Subproblem 2
Set the factor '(1 + 7rs)' equal to zero and attempt to solve:

Simplifying
1 + 7rs = 0

Solving
1 + 7rs = 0

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

Add '-1' to each side of the equation.
1 + -1 + 7rs = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 7rs = 0 + -1
7rs = 0 + -1

Combine like terms: 0 + -1 = -1
7rs = -1

Divide each side by '7s'.
r = -0.1428571429s-1

Simplifying
r = -0.1428571429s-1
Solution
r = {-0.1428571429s-1, -0.1428571429s-1}