8x-14=(x^2)+1

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

Simplifying
8x + -14 = (x2) + 1

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

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

Solving
-14 + 8x = 1 + x2

Solving for variable 'x'.

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

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

Reorder the terms:
-15 + 8x + -1x2 = 1 + -1 + x2 + -1x2

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

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

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

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

Simplifying
-5 + x = 0

Solving
-5 + x = 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 + x = 0 + 5

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

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

Simplifying
x = 5
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 = {5, 3}