x^2-5x+13=x+4

Solution for x^2-5x+13=x+4 equation:

Simplifying
x2 + -5x + 13 = x + 4

Reorder the terms:
13 + -5x + x2 = x + 4

Reorder the terms:
13 + -5x + x2 = 4 + x

Solving
13 + -5x + x2 = 4 + x

Solving for variable 'x'.

Reorder the terms:
13 + -4 + -5x + -1x + x2 = 4 + x + -4 + -1x

Combine like terms: 13 + -4 = 9
9 + -5x + -1x + x2 = 4 + x + -4 + -1x

Combine like terms: -5x + -1x = -6x
9 + -6x + x2 = 4 + x + -4 + -1x

Reorder the terms:
9 + -6x + x2 = 4 + -4 + x + -1x

Combine like terms: 4 + -4 = 0
9 + -6x + x2 = 0 + x + -1x
9 + -6x + x2 = x + -1x

Combine like terms: x + -1x = 0
9 + -6x + x2 = 0

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

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 '(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
Solution
x = {3, 3}