x^2-1=8x-17

Solution for x^2-1=8x-17 equation:

Simplifying
x2 + -1 = 8x + -17

Reorder the terms:
-1 + x2 = 8x + -17

Reorder the terms:
-1 + x2 = -17 + 8x

Solving
-1 + x2 = -17 + 8x

Solving for variable 'x'.

Reorder the terms:
-1 + 17 + -8x + x2 = -17 + 8x + 17 + -8x

Combine like terms: -1 + 17 = 16
16 + -8x + x2 = -17 + 8x + 17 + -8x

Reorder the terms:
16 + -8x + x2 = -17 + 17 + 8x + -8x

Combine like terms: -17 + 17 = 0
16 + -8x + x2 = 0 + 8x + -8x
16 + -8x + x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
16 + -8x + x2 = 0

Factor a trinomial.
(4 + -1x)(4 + -1x) = 0

Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {4, 4}