1.5X^2-0.375X-1200=0

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Solution for 1.5X^2-0.375X-1200=0 equation: 


Simplifying
1.5X2 + -0.375X + -1200 = 0

Reorder the terms:
-1200 + -0.375X + 1.5X2 = 0

Solving
-1200 + -0.375X + 1.5X2 = 0

Solving for variable 'X'.

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

Divide each side by '1.5'.
-800 + -0.25X + X2 = 0

Move the constant term to the right:

Add '800' to each side of the equation.
-800 + -0.25X + 800 + X2 = 0 + 800

Reorder the terms:
-800 + 800 + -0.25X + X2 = 0 + 800

Combine like terms: -800 + 800 = 0
0 + -0.25X + X2 = 0 + 800
-0.25X + X2 = 0 + 800

Combine like terms: 0 + 800 = 800
-0.25X + X2 = 800

The X term is -0.25X.  Take half its coefficient (-0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
-0.25X + 0.015625 + X2 = 800 + 0.015625

Reorder the terms:
0.015625 + -0.25X + X2 = 800 + 0.015625

Combine like terms: 800 + 0.015625 = 800.015625
0.015625 + -0.25X + X2 = 800.015625

Factor a perfect square on the left side:
(X + -0.125)(X + -0.125) = 800.015625

Calculate the square root of the right side: 28.28454746

Break this problem into two subproblems by setting 
(X + -0.125) equal to 28.28454746 and -28.28454746.


Subproblem 1
X + -0.125 = 28.28454746

Simplifying
X + -0.125 = 28.28454746

Reorder the terms:
-0.125 + X = 28.28454746

Solving
-0.125 + X = 28.28454746

Solving for variable 'X'.

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

Add '0.125' to each side of the equation.
-0.125 + 0.125 + X = 28.28454746 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + X = 28.28454746 + 0.125
X = 28.28454746 + 0.125

Combine like terms: 28.28454746 + 0.125 = 28.40954746
X = 28.40954746

Simplifying
X = 28.40954746


Subproblem 2
X + -0.125 = -28.28454746

Simplifying
X + -0.125 = -28.28454746

Reorder the terms:
-0.125 + X = -28.28454746

Solving
-0.125 + X = -28.28454746

Solving for variable 'X'.

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

Add '0.125' to each side of the equation.
-0.125 + 0.125 + X = -28.28454746 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + X = -28.28454746 + 0.125
X = -28.28454746 + 0.125

Combine like terms: -28.28454746 + 0.125 = -28.15954746
X = -28.15954746

Simplifying
X = -28.15954746


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {28.40954746, -28.15954746}

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