0=49x^2-14x+1

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

Simplifying
0 = 49x2 + -14x + 1

Reorder the terms:
0 = 1 + -14x + 49x2

Solving
0 = 1 + -14x + 49x2

Solving for variable 'x'.

Combine like terms: 0 + -1 = -1
-1 + 14x + -49x2 = 1 + -14x + 49x2 + -1 + 14x + -49x2

Reorder the terms:
-1 + 14x + -49x2 = 1 + -1 + -14x + 14x + 49x2 + -49x2

Combine like terms: 1 + -1 = 0
-1 + 14x + -49x2 = 0 + -14x + 14x + 49x2 + -49x2
-1 + 14x + -49x2 = -14x + 14x + 49x2 + -49x2

Combine like terms: -14x + 14x = 0
-1 + 14x + -49x2 = 0 + 49x2 + -49x2
-1 + 14x + -49x2 = 49x2 + -49x2

Combine like terms: 49x2 + -49x2 = 0
-1 + 14x + -49x2 = 0

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

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

Simplifying
-1 + 7x = 0

Solving
-1 + 7x = 0

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

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

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

Combine like terms: 0 + 1 = 1
7x = 1

Divide each side by '7'.
x = 0.1428571429

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

Simplifying
1 + -7x = 0

Solving
1 + -7x = 0

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

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

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

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

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

Simplifying
x = 0.1428571429
Solution
x = {0.1428571429, 0.1428571429}