x^2-8x+14=-1

Solution for x^2-8x+14=-1 equation:

Simplifying
x2 + -8x + 14 = -1

Reorder the terms:
14 + -8x + x2 = -1

Solving
14 + -8x + x2 = -1

Solving for variable 'x'.

Reorder the terms:
14 + 1 + -8x + x2 = -1 + 1

Combine like terms: 14 + 1 = 15
15 + -8x + x2 = -1 + 1

Combine like terms: -1 + 1 = 0
15 + -8x + x2 = 0

Factor a trinomial.
(3 + -1x)(5 + -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 '(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}