49a^2-14a+1=0

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

Simplifying
49a2 + -14a + 1 = 0

Reorder the terms:
1 + -14a + 49a2 = 0

Solving
1 + -14a + 49a2 = 0

Solving for variable 'a'.

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

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

Simplifying
1 + -7a = 0

Solving
1 + -7a = 0

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

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

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

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

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

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

Simplifying
1 + -7a = 0

Solving
1 + -7a = 0

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

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

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

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

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

Simplifying
a = 0.1428571429
Solution
a = {0.1428571429, 0.1428571429}