1.25X^2-16X-48=0

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Solution for 1.25X^2-16X-48=0 equation: 


Simplifying
1.25X2 + -16X + -48 = 0

Reorder the terms:
-48 + -16X + 1.25X2 = 0

Solving
-48 + -16X + 1.25X2 = 0

Solving for variable 'X'.

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

Divide each side by '1.25'.
-38.4 + -12.8X + X2 = 0

Move the constant term to the right:

Add '38.4' to each side of the equation.
-38.4 + -12.8X + 38.4 + X2 = 0 + 38.4

Reorder the terms:
-38.4 + 38.4 + -12.8X + X2 = 0 + 38.4

Combine like terms: -38.4 + 38.4 = 0.0
0.0 + -12.8X + X2 = 0 + 38.4
-12.8X + X2 = 0 + 38.4

Combine like terms: 0 + 38.4 = 38.4
-12.8X + X2 = 38.4

The X term is -12.8X.  Take half its coefficient (-6.4).
Square it (40.96) and add it to both sides.

Add '40.96' to each side of the equation.
-12.8X + 40.96 + X2 = 38.4 + 40.96

Reorder the terms:
40.96 + -12.8X + X2 = 38.4 + 40.96

Combine like terms: 38.4 + 40.96 = 79.36
40.96 + -12.8X + X2 = 79.36

Factor a perfect square on the left side:
(X + -6.4)(X + -6.4) = 79.36

Calculate the square root of the right side: 8.908422981

Break this problem into two subproblems by setting 
(X + -6.4) equal to 8.908422981 and -8.908422981.


Subproblem 1
X + -6.4 = 8.908422981

Simplifying
X + -6.4 = 8.908422981

Reorder the terms:
-6.4 + X = 8.908422981

Solving
-6.4 + X = 8.908422981

Solving for variable 'X'.

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

Add '6.4' to each side of the equation.
-6.4 + 6.4 + X = 8.908422981 + 6.4

Combine like terms: -6.4 + 6.4 = 0.0
0.0 + X = 8.908422981 + 6.4
X = 8.908422981 + 6.4

Combine like terms: 8.908422981 + 6.4 = 15.308422981
X = 15.308422981

Simplifying
X = 15.308422981


Subproblem 2
X + -6.4 = -8.908422981

Simplifying
X + -6.4 = -8.908422981

Reorder the terms:
-6.4 + X = -8.908422981

Solving
-6.4 + X = -8.908422981

Solving for variable 'X'.

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

Add '6.4' to each side of the equation.
-6.4 + 6.4 + X = -8.908422981 + 6.4

Combine like terms: -6.4 + 6.4 = 0.0
0.0 + X = -8.908422981 + 6.4
X = -8.908422981 + 6.4

Combine like terms: -8.908422981 + 6.4 = -2.508422981
X = -2.508422981

Simplifying
X = -2.508422981


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {15.308422981, -2.508422981}

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