49w^2-14w+1=0

Solution for 49w^2-14w+1=0 equation:

Simplifying
49w2 + -14w + 1 = 0

Reorder the terms:
1 + -14w + 49w2 = 0

Solving
1 + -14w + 49w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(1 + -7w)(1 + -7w) = 0

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

Simplifying
1 + -7w = 0

Solving
1 + -7w = 0

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

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

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

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

Divide each side by '-7'.
w = 0.1428571429

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

Simplifying
1 + -7w = 0

Solving
1 + -7w = 0

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

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

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

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

Divide each side by '-7'.
w = 0.1428571429

Simplifying
w = 0.1428571429
Solution
w = {0.1428571429, 0.1428571429}