(x-45)+(x-45)(x-45)+x+x=540

Solution for (x-45)+(x-45)(x-45)+x+x=540 equation:

Simplifying
(x + -45) + (x + -45)(x + -45) + x + x = 540

Reorder the terms:
(-45 + x) + (x + -45)(x + -45) + x + x = 540

Remove parenthesis around (-45 + x)
-45 + x + (x + -45)(x + -45) + x + x = 540

Reorder the terms:
-45 + x + (-45 + x)(x + -45) + x + x = 540

Reorder the terms:
-45 + x + (-45 + x)(-45 + x) + x + x = 540

Multiply (-45 + x) * (-45 + x)
-45 + x + (-45(-45 + x) + x(-45 + x)) + x + x = 540
-45 + x + ((-45 * -45 + x * -45) + x(-45 + x)) + x + x = 540
-45 + x + ((2025 + -45x) + x(-45 + x)) + x + x = 540
-45 + x + (2025 + -45x + (-45 * x + x * x)) + x + x = 540
-45 + x + (2025 + -45x + (-45x + x2)) + x + x = 540

Combine like terms: -45x + -45x = -90x
-45 + x + (2025 + -90x + x2) + x + x = 540

Reorder the terms:
-45 + 2025 + x + -90x + x + x + x2 = 540

Combine like terms: -45 + 2025 = 1980
1980 + x + -90x + x + x + x2 = 540

Combine like terms: x + -90x = -89x
1980 + -89x + x + x + x2 = 540

Combine like terms: -89x + x = -88x
1980 + -88x + x + x2 = 540

Combine like terms: -88x + x = -87x
1980 + -87x + x2 = 540

Solving
1980 + -87x + x2 = 540

Solving for variable 'x'.

Reorder the terms:
1980 + -540 + -87x + x2 = 540 + -540

Combine like terms: 1980 + -540 = 1440
1440 + -87x + x2 = 540 + -540

Combine like terms: 540 + -540 = 0
1440 + -87x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-1440' to each side of the equation.
1440 + -87x + -1440 + x2 = 0 + -1440

Reorder the terms:
1440 + -1440 + -87x + x2 = 0 + -1440

Combine like terms: 1440 + -1440 = 0
0 + -87x + x2 = 0 + -1440
-87x + x2 = 0 + -1440

Combine like terms: 0 + -1440 = -1440
-87x + x2 = -1440

The x term is -87x.  Take half its coefficient (-43.5).
Square it (1892.25) and add it to both sides.

Add '1892.25' to each side of the equation.
-87x + 1892.25 + x2 = -1440 + 1892.25

Reorder the terms:
1892.25 + -87x + x2 = -1440 + 1892.25

Combine like terms: -1440 + 1892.25 = 452.25
1892.25 + -87x + x2 = 452.25

Factor a perfect square on the left side:
(x + -43.5)(x + -43.5) = 452.25

Calculate the square root of the right side: 21.266170318

Break this problem into two subproblems by setting 
(x + -43.5) equal to 21.266170318 and -21.266170318.

Subproblem 1
x + -43.5 = 21.266170318

Simplifying
x + -43.5 = 21.266170318

Reorder the terms:
-43.5 + x = 21.266170318

Solving
-43.5 + x = 21.266170318

Solving for variable 'x'.

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

Add '43.5' to each side of the equation.
-43.5 + 43.5 + x = 21.266170318 + 43.5

Combine like terms: -43.5 + 43.5 = 0.0
0.0 + x = 21.266170318 + 43.5
x = 21.266170318 + 43.5

Combine like terms: 21.266170318 + 43.5 = 64.766170318
x = 64.766170318

Simplifying
x = 64.766170318

Subproblem 2
x + -43.5 = -21.266170318

Simplifying
x + -43.5 = -21.266170318

Reorder the terms:
-43.5 + x = -21.266170318

Solving
-43.5 + x = -21.266170318

Solving for variable 'x'.

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

Add '43.5' to each side of the equation.
-43.5 + 43.5 + x = -21.266170318 + 43.5

Combine like terms: -43.5 + 43.5 = 0.0
0.0 + x = -21.266170318 + 43.5
x = -21.266170318 + 43.5

Combine like terms: -21.266170318 + 43.5 = 22.233829682
x = 22.233829682

Simplifying
x = 22.233829682

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {64.766170318, 22.233829682}