289x^2+1=34x

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

Simplifying
289x2 + 1 = 34x

Reorder the terms:
1 + 289x2 = 34x

Solving
1 + 289x2 = 34x

Solving for variable 'x'.

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

Combine like terms: 34x + -34x = 0
1 + -34x + 289x2 = 0

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}