x^2-2x+13=61

Solution for x^2-2x+13=61 equation:

Simplifying
x2 + -2x + 13 = 61

Reorder the terms:
13 + -2x + x2 = 61

Solving
13 + -2x + x2 = 61

Solving for variable 'x'.

Reorder the terms:
13 + -61 + -2x + x2 = 61 + -61

Combine like terms: 13 + -61 = -48
-48 + -2x + x2 = 61 + -61

Combine like terms: 61 + -61 = 0
-48 + -2x + x2 = 0

Factor a trinomial.
(-6 + -1x)(8 + -1x) = 0

Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6
Subproblem 2
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
Solution
x = {-6, 8}