180=X(X-4)+2(2-X)

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Solution for 180=X(X-4)+2(2-X) equation: 


Simplifying
180 = X(X + -4) + 2(2 + -1X)

Reorder the terms:
180 = X(-4 + X) + 2(2 + -1X)
180 = (-4 * X + X * X) + 2(2 + -1X)
180 = (-4X + X2) + 2(2 + -1X)
180 = -4X + X2 + (2 * 2 + -1X * 2)
180 = -4X + X2 + (4 + -2X)

Reorder the terms:
180 = 4 + -4X + -2X + X2

Combine like terms: -4X + -2X = -6X
180 = 4 + -6X + X2

Solving
180 = 4 + -6X + X2

Solving for variable 'X'.

Combine like terms: 180 + -4 = 176
176 + 6X + -1X2 = 4 + -6X + X2 + -4 + 6X + -1X2

Reorder the terms:
176 + 6X + -1X2 = 4 + -4 + -6X + 6X + X2 + -1X2

Combine like terms: 4 + -4 = 0
176 + 6X + -1X2 = 0 + -6X + 6X + X2 + -1X2
176 + 6X + -1X2 = -6X + 6X + X2 + -1X2

Combine like terms: -6X + 6X = 0
176 + 6X + -1X2 = 0 + X2 + -1X2
176 + 6X + -1X2 = X2 + -1X2

Combine like terms: X2 + -1X2 = 0
176 + 6X + -1X2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-176 + -6X + X2 = 0

Move the constant term to the right:

Add '176' to each side of the equation.
-176 + -6X + 176 + X2 = 0 + 176

Reorder the terms:
-176 + 176 + -6X + X2 = 0 + 176

Combine like terms: -176 + 176 = 0
0 + -6X + X2 = 0 + 176
-6X + X2 = 0 + 176

Combine like terms: 0 + 176 = 176
-6X + X2 = 176

The X term is -6X.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6X + 9 + X2 = 176 + 9

Reorder the terms:
9 + -6X + X2 = 176 + 9

Combine like terms: 176 + 9 = 185
9 + -6X + X2 = 185

Factor a perfect square on the left side:
(X + -3)(X + -3) = 185

Calculate the square root of the right side: 13.601470509

Break this problem into two subproblems by setting 
(X + -3) equal to 13.601470509 and -13.601470509.


Subproblem 1
X + -3 = 13.601470509

Simplifying
X + -3 = 13.601470509

Reorder the terms:
-3 + X = 13.601470509

Solving
-3 + X = 13.601470509

Solving for variable 'X'.

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

Add '3' to each side of the equation.
-3 + 3 + X = 13.601470509 + 3

Combine like terms: -3 + 3 = 0
0 + X = 13.601470509 + 3
X = 13.601470509 + 3

Combine like terms: 13.601470509 + 3 = 16.601470509
X = 16.601470509

Simplifying
X = 16.601470509


Subproblem 2
X + -3 = -13.601470509

Simplifying
X + -3 = -13.601470509

Reorder the terms:
-3 + X = -13.601470509

Solving
-3 + X = -13.601470509

Solving for variable 'X'.

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

Add '3' to each side of the equation.
-3 + 3 + X = -13.601470509 + 3

Combine like terms: -3 + 3 = 0
0 + X = -13.601470509 + 3
X = -13.601470509 + 3

Combine like terms: -13.601470509 + 3 = -10.601470509
X = -10.601470509

Simplifying
X = -10.601470509


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {16.601470509, -10.601470509}

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