x(x+29)+2(x+x+29)=369

Solution for x(x+29)+2(x+x+29)=369 equation:

Simplifying
x(x + 29) + 2(x + x + 29) = 369

Reorder the terms:
x(29 + x) + 2(x + x + 29) = 369
(29 * x + x * x) + 2(x + x + 29) = 369
(29x + x2) + 2(x + x + 29) = 369

Reorder the terms:
29x + x2 + 2(29 + x + x) = 369

Combine like terms: x + x = 2x
29x + x2 + 2(29 + 2x) = 369
29x + x2 + (29 * 2 + 2x * 2) = 369
29x + x2 + (58 + 4x) = 369

Reorder the terms:
58 + 29x + 4x + x2 = 369

Combine like terms: 29x + 4x = 33x
58 + 33x + x2 = 369

Solving
58 + 33x + x2 = 369

Solving for variable 'x'.

Reorder the terms:
58 + -369 + 33x + x2 = 369 + -369

Combine like terms: 58 + -369 = -311
-311 + 33x + x2 = 369 + -369

Combine like terms: 369 + -369 = 0
-311 + 33x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '311' to each side of the equation.
-311 + 33x + 311 + x2 = 0 + 311

Reorder the terms:
-311 + 311 + 33x + x2 = 0 + 311

Combine like terms: -311 + 311 = 0
0 + 33x + x2 = 0 + 311
33x + x2 = 0 + 311

Combine like terms: 0 + 311 = 311
33x + x2 = 311

The x term is 33x.  Take half its coefficient (16.5).
Square it (272.25) and add it to both sides.

Add '272.25' to each side of the equation.
33x + 272.25 + x2 = 311 + 272.25

Reorder the terms:
272.25 + 33x + x2 = 311 + 272.25

Combine like terms: 311 + 272.25 = 583.25
272.25 + 33x + x2 = 583.25

Factor a perfect square on the left side:
(x + 16.5)(x + 16.5) = 583.25

Calculate the square root of the right side: 24.150569351

Break this problem into two subproblems by setting 
(x + 16.5) equal to 24.150569351 and -24.150569351.

Subproblem 1
x + 16.5 = 24.150569351

Simplifying
x + 16.5 = 24.150569351

Reorder the terms:
16.5 + x = 24.150569351

Solving
16.5 + x = 24.150569351

Solving for variable 'x'.

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

Add '-16.5' to each side of the equation.
16.5 + -16.5 + x = 24.150569351 + -16.5

Combine like terms: 16.5 + -16.5 = 0.0
0.0 + x = 24.150569351 + -16.5
x = 24.150569351 + -16.5

Combine like terms: 24.150569351 + -16.5 = 7.650569351
x = 7.650569351

Simplifying
x = 7.650569351

Subproblem 2
x + 16.5 = -24.150569351

Simplifying
x + 16.5 = -24.150569351

Reorder the terms:
16.5 + x = -24.150569351

Solving
16.5 + x = -24.150569351

Solving for variable 'x'.

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

Add '-16.5' to each side of the equation.
16.5 + -16.5 + x = -24.150569351 + -16.5

Combine like terms: 16.5 + -16.5 = 0.0
0.0 + x = -24.150569351 + -16.5
x = -24.150569351 + -16.5

Combine like terms: -24.150569351 + -16.5 = -40.650569351
x = -40.650569351

Simplifying
x = -40.650569351

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.650569351, -40.650569351}