x^2-2x+9=89

Solution for x^2-2x+9=89 equation:

Simplifying
x2 + -2x + 9 = 89

Reorder the terms:
9 + -2x + x2 = 89

Solving
9 + -2x + x2 = 89

Solving for variable 'x'.

Reorder the terms:
9 + -89 + -2x + x2 = 89 + -89

Combine like terms: 9 + -89 = -80
-80 + -2x + x2 = 89 + -89

Combine like terms: 89 + -89 = 0
-80 + -2x + x2 = 0

Factor a trinomial.
(-8 + -1x)(10 + -1x) = 0

Subproblem 1
Set the factor '(-8 + -1x)' equal to zero and attempt to solve:

Simplifying
-8 + -1x = 0

Solving
-8 + -1x = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1x = 0 + 8

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

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

Divide each side by '-1'.
x = -8

Simplifying
x = -8
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 = {-8, 10}