2x(x+8)+x=180

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Solution for 2x(x+8)+x=180 equation: 


Simplifying
2x(x + 8) + x = 180

Reorder the terms:
2x(8 + x) + x = 180
(8 * 2x + x * 2x) + x = 180
(16x + 2x2) + x = 180

Reorder the terms:
16x + x + 2x2 = 180

Combine like terms: 16x + x = 17x
17x + 2x2 = 180

Solving
17x + 2x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + 17x + 2x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + 17x + 2x2 = 0

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

Divide each side by '2'.
-90 + 8.5x + x2 = 0

Move the constant term to the right:

Add '90' to each side of the equation.
-90 + 8.5x + 90 + x2 = 0 + 90

Reorder the terms:
-90 + 90 + 8.5x + x2 = 0 + 90

Combine like terms: -90 + 90 = 0
0 + 8.5x + x2 = 0 + 90
8.5x + x2 = 0 + 90

Combine like terms: 0 + 90 = 90
8.5x + x2 = 90

The x term is 8.5x.  Take half its coefficient (4.25).
Square it (18.0625) and add it to both sides.

Add '18.0625' to each side of the equation.
8.5x + 18.0625 + x2 = 90 + 18.0625

Reorder the terms:
18.0625 + 8.5x + x2 = 90 + 18.0625

Combine like terms: 90 + 18.0625 = 108.0625
18.0625 + 8.5x + x2 = 108.0625

Factor a perfect square on the left side:
(x + 4.25)(x + 4.25) = 108.0625

Calculate the square root of the right side: 10.395311443

Break this problem into two subproblems by setting 
(x + 4.25) equal to 10.395311443 and -10.395311443.


Subproblem 1
x + 4.25 = 10.395311443

Simplifying
x + 4.25 = 10.395311443

Reorder the terms:
4.25 + x = 10.395311443

Solving
4.25 + x = 10.395311443

Solving for variable 'x'.

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

Add '-4.25' to each side of the equation.
4.25 + -4.25 + x = 10.395311443 + -4.25

Combine like terms: 4.25 + -4.25 = 0.00
0.00 + x = 10.395311443 + -4.25
x = 10.395311443 + -4.25

Combine like terms: 10.395311443 + -4.25 = 6.145311443
x = 6.145311443

Simplifying
x = 6.145311443


Subproblem 2
x + 4.25 = -10.395311443

Simplifying
x + 4.25 = -10.395311443

Reorder the terms:
4.25 + x = -10.395311443

Solving
4.25 + x = -10.395311443

Solving for variable 'x'.

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

Add '-4.25' to each side of the equation.
4.25 + -4.25 + x = -10.395311443 + -4.25

Combine like terms: 4.25 + -4.25 = 0.00
0.00 + x = -10.395311443 + -4.25
x = -10.395311443 + -4.25

Combine like terms: -10.395311443 + -4.25 = -14.645311443
x = -14.645311443

Simplifying
x = -14.645311443


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.145311443, -14.645311443}

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