200X-3X^2-50X+100=0

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Solution for 200X-3X^2-50X+100=0 equation: 


Simplifying
200X + -3X2 + -50X + 100 = 0

Reorder the terms:
100 + 200X + -50X + -3X2 = 0

Combine like terms: 200X + -50X = 150X
100 + 150X + -3X2 = 0

Solving
100 + 150X + -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'.
-33.33333333 + -50X + X2 = 0

Move the constant term to the right:

Add '33.33333333' to each side of the equation.
-33.33333333 + -50X + 33.33333333 + X2 = 0 + 33.33333333

Reorder the terms:
-33.33333333 + 33.33333333 + -50X + X2 = 0 + 33.33333333

Combine like terms: -33.33333333 + 33.33333333 = 0.00000000
0.00000000 + -50X + X2 = 0 + 33.33333333
-50X + X2 = 0 + 33.33333333

Combine like terms: 0 + 33.33333333 = 33.33333333
-50X + X2 = 33.33333333

The X term is -50X.  Take half its coefficient (-25).
Square it (625) and add it to both sides.

Add '625' to each side of the equation.
-50X + 625 + X2 = 33.33333333 + 625

Reorder the terms:
625 + -50X + X2 = 33.33333333 + 625

Combine like terms: 33.33333333 + 625 = 658.33333333
625 + -50X + X2 = 658.33333333

Factor a perfect square on the left side:
(X + -25)(X + -25) = 658.33333333

Calculate the square root of the right side: 25.658007197

Break this problem into two subproblems by setting 
(X + -25) equal to 25.658007197 and -25.658007197.


Subproblem 1
X + -25 = 25.658007197

Simplifying
X + -25 = 25.658007197

Reorder the terms:
-25 + X = 25.658007197

Solving
-25 + X = 25.658007197

Solving for variable 'X'.

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

Add '25' to each side of the equation.
-25 + 25 + X = 25.658007197 + 25

Combine like terms: -25 + 25 = 0
0 + X = 25.658007197 + 25
X = 25.658007197 + 25

Combine like terms: 25.658007197 + 25 = 50.658007197
X = 50.658007197

Simplifying
X = 50.658007197


Subproblem 2
X + -25 = -25.658007197

Simplifying
X + -25 = -25.658007197

Reorder the terms:
-25 + X = -25.658007197

Solving
-25 + X = -25.658007197

Solving for variable 'X'.

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

Add '25' to each side of the equation.
-25 + 25 + X = -25.658007197 + 25

Combine like terms: -25 + 25 = 0
0 + X = -25.658007197 + 25
X = -25.658007197 + 25

Combine like terms: -25.658007197 + 25 = -0.658007197
X = -0.658007197

Simplifying
X = -0.658007197


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {50.658007197, -0.658007197}

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