x^2-9=11x-37

Solution for x^2-9=11x-37 equation:

Simplifying
x2 + -9 = 11x + -37

Reorder the terms:
-9 + x2 = 11x + -37

Reorder the terms:
-9 + x2 = -37 + 11x

Solving
-9 + x2 = -37 + 11x

Solving for variable 'x'.

Reorder the terms:
-9 + 37 + -11x + x2 = -37 + 11x + 37 + -11x

Combine like terms: -9 + 37 = 28
28 + -11x + x2 = -37 + 11x + 37 + -11x

Reorder the terms:
28 + -11x + x2 = -37 + 37 + 11x + -11x

Combine like terms: -37 + 37 = 0
28 + -11x + x2 = 0 + 11x + -11x
28 + -11x + x2 = 11x + -11x

Combine like terms: 11x + -11x = 0
28 + -11x + x2 = 0

Factor a trinomial.
(4 + -1x)(7 + -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 '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {4, 7}