(x+3)2+(x-8)(x-1)=16

Solution for (x+3)2+(x-8)(x-1)=16 equation:

Simplifying
(x + 3) * 2 + (x + -8)(x + -1) = 16

Reorder the terms:
(3 + x) * 2 + (x + -8)(x + -1) = 16

Reorder the terms for easier multiplication:
2(3 + x) + (x + -8)(x + -1) = 16
(3 * 2 + x * 2) + (x + -8)(x + -1) = 16
(6 + 2x) + (x + -8)(x + -1) = 16

Reorder the terms:
6 + 2x + (-8 + x)(x + -1) = 16

Reorder the terms:
6 + 2x + (-8 + x)(-1 + x) = 16

Multiply (-8 + x) * (-1 + x)
6 + 2x + (-8(-1 + x) + x(-1 + x)) = 16
6 + 2x + ((-1 * -8 + x * -8) + x(-1 + x)) = 16
6 + 2x + ((8 + -8x) + x(-1 + x)) = 16
6 + 2x + (8 + -8x + (-1 * x + x * x)) = 16
6 + 2x + (8 + -8x + (-1x + x2)) = 16

Combine like terms: -8x + -1x = -9x
6 + 2x + (8 + -9x + x2) = 16

Reorder the terms:
6 + 8 + 2x + -9x + x2 = 16

Combine like terms: 6 + 8 = 14
14 + 2x + -9x + x2 = 16

Combine like terms: 2x + -9x = -7x
14 + -7x + x2 = 16

Solving
14 + -7x + x2 = 16

Solving for variable 'x'.

Reorder the terms:
14 + -16 + -7x + x2 = 16 + -16

Combine like terms: 14 + -16 = -2
-2 + -7x + x2 = 16 + -16

Combine like terms: 16 + -16 = 0
-2 + -7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -7x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + -7x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -7x + x2 = 0 + 2
-7x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
-7x + x2 = 2

The x term is -7x.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7x + 12.25 + x2 = 2 + 12.25

Reorder the terms:
12.25 + -7x + x2 = 2 + 12.25

Combine like terms: 2 + 12.25 = 14.25
12.25 + -7x + x2 = 14.25

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 14.25

Calculate the square root of the right side: 3.774917218

Break this problem into two subproblems by setting 
(x + -3.5) equal to 3.774917218 and -3.774917218.

Subproblem 1
x + -3.5 = 3.774917218

Simplifying
x + -3.5 = 3.774917218

Reorder the terms:
-3.5 + x = 3.774917218

Solving
-3.5 + x = 3.774917218

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = 3.774917218 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = 3.774917218 + 3.5
x = 3.774917218 + 3.5

Combine like terms: 3.774917218 + 3.5 = 7.274917218
x = 7.274917218

Simplifying
x = 7.274917218

Subproblem 2
x + -3.5 = -3.774917218

Simplifying
x + -3.5 = -3.774917218

Reorder the terms:
-3.5 + x = -3.774917218

Solving
-3.5 + x = -3.774917218

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = -3.774917218 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = -3.774917218 + 3.5
x = -3.774917218 + 3.5

Combine like terms: -3.774917218 + 3.5 = -0.274917218
x = -0.274917218

Simplifying
x = -0.274917218

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.274917218, -0.274917218}