289x^2+34x+1=0

Solution for 289x^2+34x+1=0 equation:

Simplifying
289x2 + 34x + 1 = 0

Reorder the terms:
1 + 34x + 289x2 = 0

Solving
1 + 34x + 289x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(1 + 17x)(1 + 17x) = 0

Subproblem 1
Set the factor '(1 + 17x)' equal to zero and attempt to solve:

Simplifying
1 + 17x = 0

Solving
1 + 17x = 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 + 17x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 17x = 0 + -1
17x = 0 + -1

Combine like terms: 0 + -1 = -1
17x = -1

Divide each side by '17'.
x = -0.05882352941

Simplifying
x = -0.05882352941
Subproblem 2
Set the factor '(1 + 17x)' equal to zero and attempt to solve:

Simplifying
1 + 17x = 0

Solving
1 + 17x = 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 + 17x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 17x = 0 + -1
17x = 0 + -1

Combine like terms: 0 + -1 = -1
17x = -1

Divide each side by '17'.
x = -0.05882352941

Simplifying
x = -0.05882352941
Solution
x = {-0.05882352941, -0.05882352941}