3X^2-400X+3600=0

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Solution for 3X^2-400X+3600=0 equation: 


Simplifying
3X2 + -400X + 3600 = 0

Reorder the terms:
3600 + -400X + 3X2 = 0

Solving
3600 + -400X + 3X2 = 0

Solving for variable 'X'.

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

Divide each side by '3'.
1200 + -133.3333333X + X2 = 0

Move the constant term to the right:

Add '-1200' to each side of the equation.
1200 + -133.3333333X + -1200 + X2 = 0 + -1200

Reorder the terms:
1200 + -1200 + -133.3333333X + X2 = 0 + -1200

Combine like terms: 1200 + -1200 = 0
0 + -133.3333333X + X2 = 0 + -1200
-133.3333333X + X2 = 0 + -1200

Combine like terms: 0 + -1200 = -1200
-133.3333333X + X2 = -1200

The X term is -133.3333333X.  Take half its coefficient (-66.66666665).
Square it (4444.444442) and add it to both sides.

Add '4444.444442' to each side of the equation.
-133.3333333X + 4444.444442 + X2 = -1200 + 4444.444442

Reorder the terms:
4444.444442 + -133.3333333X + X2 = -1200 + 4444.444442

Combine like terms: -1200 + 4444.444442 = 3244.444442
4444.444442 + -133.3333333X + X2 = 3244.444442

Factor a perfect square on the left side:
(X + -66.66666665)(X + -66.66666665) = 3244.444442

Calculate the square root of the right side: 56.960024947

Break this problem into two subproblems by setting 
(X + -66.66666665) equal to 56.960024947 and -56.960024947.


Subproblem 1
X + -66.66666665 = 56.960024947

Simplifying
X + -66.66666665 = 56.960024947

Reorder the terms:
-66.66666665 + X = 56.960024947

Solving
-66.66666665 + X = 56.960024947

Solving for variable 'X'.

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

Add '66.66666665' to each side of the equation.
-66.66666665 + 66.66666665 + X = 56.960024947 + 66.66666665

Combine like terms: -66.66666665 + 66.66666665 = 0.00000000
0.00000000 + X = 56.960024947 + 66.66666665
X = 56.960024947 + 66.66666665

Combine like terms: 56.960024947 + 66.66666665 = 123.626691597
X = 123.626691597

Simplifying
X = 123.626691597


Subproblem 2
X + -66.66666665 = -56.960024947

Simplifying
X + -66.66666665 = -56.960024947

Reorder the terms:
-66.66666665 + X = -56.960024947

Solving
-66.66666665 + X = -56.960024947

Solving for variable 'X'.

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

Add '66.66666665' to each side of the equation.
-66.66666665 + 66.66666665 + X = -56.960024947 + 66.66666665

Combine like terms: -66.66666665 + 66.66666665 = 0.00000000
0.00000000 + X = -56.960024947 + 66.66666665
X = -56.960024947 + 66.66666665

Combine like terms: -56.960024947 + 66.66666665 = 9.706641703
X = 9.706641703

Simplifying
X = 9.706641703


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {123.626691597, 9.706641703}

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