x+x^2-14x+49=19

Solution for x+x^2-14x+49=19 equation:

Simplifying
x + x2 + -14x + 49 = 19

Reorder the terms:
49 + x + -14x + x2 = 19

Combine like terms: x + -14x = -13x
49 + -13x + x2 = 19

Solving
49 + -13x + x2 = 19

Solving for variable 'x'.

Reorder the terms:
49 + -19 + -13x + x2 = 19 + -19

Combine like terms: 49 + -19 = 30
30 + -13x + x2 = 19 + -19

Combine like terms: 19 + -19 = 0
30 + -13x + x2 = 0

Factor a trinomial.
(3 + -1x)(10 + -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 '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {3, 10}