(x+9)(x-1)=33

Solution for (x+9)(x-1)=33 equation:

Simplifying
(x + 9)(x + -1) = 33

Reorder the terms:
(9 + x)(x + -1) = 33

Reorder the terms:
(9 + x)(-1 + x) = 33

Multiply (9 + x) * (-1 + x)
(9(-1 + x) + x(-1 + x)) = 33
((-1 * 9 + x * 9) + x(-1 + x)) = 33
((-9 + 9x) + x(-1 + x)) = 33
(-9 + 9x + (-1 * x + x * x)) = 33
(-9 + 9x + (-1x + x2)) = 33

Combine like terms: 9x + -1x = 8x
(-9 + 8x + x2) = 33

Solving
-9 + 8x + x2 = 33

Solving for variable 'x'.

Reorder the terms:
-9 + -33 + 8x + x2 = 33 + -33

Combine like terms: -9 + -33 = -42
-42 + 8x + x2 = 33 + -33

Combine like terms: 33 + -33 = 0
-42 + 8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '42' to each side of the equation.
-42 + 8x + 42 + x2 = 0 + 42

Reorder the terms:
-42 + 42 + 8x + x2 = 0 + 42

Combine like terms: -42 + 42 = 0
0 + 8x + x2 = 0 + 42
8x + x2 = 0 + 42

Combine like terms: 0 + 42 = 42
8x + x2 = 42

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = 42 + 16

Reorder the terms:
16 + 8x + x2 = 42 + 16

Combine like terms: 42 + 16 = 58
16 + 8x + x2 = 58

Factor a perfect square on the left side:
(x + 4)(x + 4) = 58

Calculate the square root of the right side: 7.615773106

Break this problem into two subproblems by setting 
(x + 4) equal to 7.615773106 and -7.615773106.

Subproblem 1
x + 4 = 7.615773106

Simplifying
x + 4 = 7.615773106

Reorder the terms:
4 + x = 7.615773106

Solving
4 + x = 7.615773106

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = 7.615773106 + -4

Combine like terms: 4 + -4 = 0
0 + x = 7.615773106 + -4
x = 7.615773106 + -4

Combine like terms: 7.615773106 + -4 = 3.615773106
x = 3.615773106

Simplifying
x = 3.615773106

Subproblem 2
x + 4 = -7.615773106

Simplifying
x + 4 = -7.615773106

Reorder the terms:
4 + x = -7.615773106

Solving
4 + x = -7.615773106

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = -7.615773106 + -4

Combine like terms: 4 + -4 = 0
0 + x = -7.615773106 + -4
x = -7.615773106 + -4

Combine like terms: -7.615773106 + -4 = -11.615773106
x = -11.615773106

Simplifying
x = -11.615773106

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.615773106, -11.615773106}