x(x)+(x+4)(x+4)=841

Solution for x(x)+(x+4)(x+4)=841 equation:

Simplifying
x(x) + (x + 4)(x + 4) = 841

Multiply x * x
x2 + (x + 4)(x + 4) = 841

Reorder the terms:
x2 + (4 + x)(x + 4) = 841

Reorder the terms:
x2 + (4 + x)(4 + x) = 841

Multiply (4 + x) * (4 + x)
x2 + (4(4 + x) + x(4 + x)) = 841
x2 + ((4 * 4 + x * 4) + x(4 + x)) = 841
x2 + ((16 + 4x) + x(4 + x)) = 841
x2 + (16 + 4x + (4 * x + x * x)) = 841
x2 + (16 + 4x + (4x + x2)) = 841

Combine like terms: 4x + 4x = 8x
x2 + (16 + 8x + x2) = 841

Reorder the terms:
16 + 8x + x2 + x2 = 841

Combine like terms: x2 + x2 = 2x2
16 + 8x + 2x2 = 841

Solving
16 + 8x + 2x2 = 841

Solving for variable 'x'.

Reorder the terms:
16 + -841 + 8x + 2x2 = 841 + -841

Combine like terms: 16 + -841 = -825
-825 + 8x + 2x2 = 841 + -841

Combine like terms: 841 + -841 = 0
-825 + 8x + 2x2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-412.5 + 4x + x2 = 0

Move the constant term to the right:

Add '412.5' to each side of the equation.
-412.5 + 4x + 412.5 + x2 = 0 + 412.5

Reorder the terms:
-412.5 + 412.5 + 4x + x2 = 0 + 412.5

Combine like terms: -412.5 + 412.5 = 0.0
0.0 + 4x + x2 = 0 + 412.5
4x + x2 = 0 + 412.5

Combine like terms: 0 + 412.5 = 412.5
4x + x2 = 412.5

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 412.5 + 4

Reorder the terms:
4 + 4x + x2 = 412.5 + 4

Combine like terms: 412.5 + 4 = 416.5
4 + 4x + x2 = 416.5

Factor a perfect square on the left side:
(x + 2)(x + 2) = 416.5

Calculate the square root of the right side: 20.408331632

Break this problem into two subproblems by setting 
(x + 2) equal to 20.408331632 and -20.408331632.

Subproblem 1
x + 2 = 20.408331632

Simplifying
x + 2 = 20.408331632

Reorder the terms:
2 + x = 20.408331632

Solving
2 + x = 20.408331632

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = 20.408331632 + -2

Combine like terms: 2 + -2 = 0
0 + x = 20.408331632 + -2
x = 20.408331632 + -2

Combine like terms: 20.408331632 + -2 = 18.408331632
x = 18.408331632

Simplifying
x = 18.408331632

Subproblem 2
x + 2 = -20.408331632

Simplifying
x + 2 = -20.408331632

Reorder the terms:
2 + x = -20.408331632

Solving
2 + x = -20.408331632

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = -20.408331632 + -2

Combine like terms: 2 + -2 = 0
0 + x = -20.408331632 + -2
x = -20.408331632 + -2

Combine like terms: -20.408331632 + -2 = -22.408331632
x = -22.408331632

Simplifying
x = -22.408331632

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {18.408331632, -22.408331632}