x^2+289-34x+x^2=145

Solution for x^2+289-34x+x^2=145 equation:

Simplifying
x2 + 289 + -34x + x2 = 145

Reorder the terms:
289 + -34x + x2 + x2 = 145

Combine like terms: x2 + x2 = 2x2
289 + -34x + 2x2 = 145

Solving
289 + -34x + 2x2 = 145

Solving for variable 'x'.

Reorder the terms:
289 + -145 + -34x + 2x2 = 145 + -145

Combine like terms: 289 + -145 = 144
144 + -34x + 2x2 = 145 + -145

Combine like terms: 145 + -145 = 0
144 + -34x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(72 + -17x + x2) = 0

Factor a trinomial.
2((8 + -1x)(9 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Subproblem 2
Set the factor '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {8, 9}