x(x-8)-13(x+2)-3=

Solution for x(x-8)-13(x+2)-3= equation:

Simplifying
x(x + -8) + -13(x + 2) + -3 = 0

Reorder the terms:
x(-8 + x) + -13(x + 2) + -3 = 0
(-8 * x + x * x) + -13(x + 2) + -3 = 0
(-8x + x2) + -13(x + 2) + -3 = 0

Reorder the terms:
-8x + x2 + -13(2 + x) + -3 = 0
-8x + x2 + (2 * -13 + x * -13) + -3 = 0
-8x + x2 + (-26 + -13x) + -3 = 0

Reorder the terms:
-26 + -3 + -8x + -13x + x2 = 0

Combine like terms: -26 + -3 = -29
-29 + -8x + -13x + x2 = 0

Combine like terms: -8x + -13x = -21x
-29 + -21x + x2 = 0

Solving
-29 + -21x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '29' to each side of the equation.
-29 + -21x + 29 + x2 = 0 + 29

Reorder the terms:
-29 + 29 + -21x + x2 = 0 + 29

Combine like terms: -29 + 29 = 0
0 + -21x + x2 = 0 + 29
-21x + x2 = 0 + 29

Combine like terms: 0 + 29 = 29
-21x + x2 = 29

The x term is -21x.  Take half its coefficient (-10.5).
Square it (110.25) and add it to both sides.

Add '110.25' to each side of the equation.
-21x + 110.25 + x2 = 29 + 110.25

Reorder the terms:
110.25 + -21x + x2 = 29 + 110.25

Combine like terms: 29 + 110.25 = 139.25
110.25 + -21x + x2 = 139.25

Factor a perfect square on the left side:
(x + -10.5)(x + -10.5) = 139.25

Calculate the square root of the right side: 11.800423721

Break this problem into two subproblems by setting 
(x + -10.5) equal to 11.800423721 and -11.800423721.

Subproblem 1
x + -10.5 = 11.800423721

Simplifying
x + -10.5 = 11.800423721

Reorder the terms:
-10.5 + x = 11.800423721

Solving
-10.5 + x = 11.800423721

Solving for variable 'x'.

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

Add '10.5' to each side of the equation.
-10.5 + 10.5 + x = 11.800423721 + 10.5

Combine like terms: -10.5 + 10.5 = 0.0
0.0 + x = 11.800423721 + 10.5
x = 11.800423721 + 10.5

Combine like terms: 11.800423721 + 10.5 = 22.300423721
x = 22.300423721

Simplifying
x = 22.300423721

Subproblem 2
x + -10.5 = -11.800423721

Simplifying
x + -10.5 = -11.800423721

Reorder the terms:
-10.5 + x = -11.800423721

Solving
-10.5 + x = -11.800423721

Solving for variable 'x'.

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

Add '10.5' to each side of the equation.
-10.5 + 10.5 + x = -11.800423721 + 10.5

Combine like terms: -10.5 + 10.5 = 0.0
0.0 + x = -11.800423721 + 10.5
x = -11.800423721 + 10.5

Combine like terms: -11.800423721 + 10.5 = -1.300423721
x = -1.300423721

Simplifying
x = -1.300423721

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {22.300423721, -1.300423721}