x^2+x^2-16x+64=34

Solution for x^2+x^2-16x+64=34 equation:

Simplifying
x2 + x2 + -16x + 64 = 34

Reorder the terms:
64 + -16x + x2 + x2 = 34

Combine like terms: x2 + x2 = 2x2
64 + -16x + 2x2 = 34

Solving
64 + -16x + 2x2 = 34

Solving for variable 'x'.

Reorder the terms:
64 + -34 + -16x + 2x2 = 34 + -34

Combine like terms: 64 + -34 = 30
30 + -16x + 2x2 = 34 + -34

Combine like terms: 34 + -34 = 0
30 + -16x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(15 + -8x + x2) = 0

Factor a trinomial.
2((3 + -1x)(5 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {3, 5}