3(X-2)(X-2)=40

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Solution for 3(X-2)(X-2)=40 equation: 


Simplifying
3(X + -2)(X + -2) = 40

Reorder the terms:
3(-2 + X)(X + -2) = 40

Reorder the terms:
3(-2 + X)(-2 + X) = 40

Multiply (-2 + X) * (-2 + X)
3(-2(-2 + X) + X(-2 + X)) = 40
3((-2 * -2 + X * -2) + X(-2 + X)) = 40
3((4 + -2X) + X(-2 + X)) = 40
3(4 + -2X + (-2 * X + X * X)) = 40
3(4 + -2X + (-2X + X2)) = 40

Combine like terms: -2X + -2X = -4X
3(4 + -4X + X2) = 40
(4 * 3 + -4X * 3 + X2 * 3) = 40
(12 + -12X + 3X2) = 40

Solving
12 + -12X + 3X2 = 40

Solving for variable 'X'.

Reorder the terms:
12 + -40 + -12X + 3X2 = 40 + -40

Combine like terms: 12 + -40 = -28
-28 + -12X + 3X2 = 40 + -40

Combine like terms: 40 + -40 = 0
-28 + -12X + 3X2 = 0

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

Divide each side by '3'.
-9.333333333 + -4X + X2 = 0

Move the constant term to the right:

Add '9.333333333' to each side of the equation.
-9.333333333 + -4X + 9.333333333 + X2 = 0 + 9.333333333

Reorder the terms:
-9.333333333 + 9.333333333 + -4X + X2 = 0 + 9.333333333

Combine like terms: -9.333333333 + 9.333333333 = 0.000000000
0.000000000 + -4X + X2 = 0 + 9.333333333
-4X + X2 = 0 + 9.333333333

Combine like terms: 0 + 9.333333333 = 9.333333333
-4X + X2 = 9.333333333

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 = 9.333333333 + 4

Reorder the terms:
4 + -4X + X2 = 9.333333333 + 4

Combine like terms: 9.333333333 + 4 = 13.333333333
4 + -4X + X2 = 13.333333333

Factor a perfect square on the left side:
(X + -2)(X + -2) = 13.333333333

Calculate the square root of the right side: 3.651483717

Break this problem into two subproblems by setting 
(X + -2) equal to 3.651483717 and -3.651483717.


Subproblem 1
X + -2 = 3.651483717

Simplifying
X + -2 = 3.651483717

Reorder the terms:
-2 + X = 3.651483717

Solving
-2 + X = 3.651483717

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 = 3.651483717 + 2

Combine like terms: -2 + 2 = 0
0 + X = 3.651483717 + 2
X = 3.651483717 + 2

Combine like terms: 3.651483717 + 2 = 5.651483717
X = 5.651483717

Simplifying
X = 5.651483717


Subproblem 2
X + -2 = -3.651483717

Simplifying
X + -2 = -3.651483717

Reorder the terms:
-2 + X = -3.651483717

Solving
-2 + X = -3.651483717

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 = -3.651483717 + 2

Combine like terms: -2 + 2 = 0
0 + X = -3.651483717 + 2
X = -3.651483717 + 2

Combine like terms: -3.651483717 + 2 = -1.651483717
X = -1.651483717

Simplifying
X = -1.651483717


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {5.651483717, -1.651483717}

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