x^2+5=8x+14

Solution for x^2+5=8x+14 equation:

Simplifying
x2 + 5 = 8x + 14

Reorder the terms:
5 + x2 = 8x + 14

Reorder the terms:
5 + x2 = 14 + 8x

Solving
5 + x2 = 14 + 8x

Solving for variable 'x'.

Reorder the terms:
5 + -14 + -8x + x2 = 14 + 8x + -14 + -8x

Combine like terms: 5 + -14 = -9
-9 + -8x + x2 = 14 + 8x + -14 + -8x

Reorder the terms:
-9 + -8x + x2 = 14 + -14 + 8x + -8x

Combine like terms: 14 + -14 = 0
-9 + -8x + x2 = 0 + 8x + -8x
-9 + -8x + x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
-9 + -8x + x2 = 0

Factor a trinomial.
(-1 + -1x)(9 + -1x) = 0

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

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 0

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

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

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

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

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

Simplifying
x = -1
Subproblem 2
Set the factor '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

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

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

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {-1, 9}