4X^2+3.8X-7.88=0

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Solution for 4X^2+3.8X-7.88=0 equation: 


Simplifying
4X2 + 3.8X + -7.88 = 0

Reorder the terms:
-7.88 + 3.8X + 4X2 = 0

Solving
-7.88 + 3.8X + 4X2 = 0

Solving for variable 'X'.

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

Divide each side by '4'.
-1.97 + 0.95X + X2 = 0

Move the constant term to the right:

Add '1.97' to each side of the equation.
-1.97 + 0.95X + 1.97 + X2 = 0 + 1.97

Reorder the terms:
-1.97 + 1.97 + 0.95X + X2 = 0 + 1.97

Combine like terms: -1.97 + 1.97 = 0.00
0.00 + 0.95X + X2 = 0 + 1.97
0.95X + X2 = 0 + 1.97

Combine like terms: 0 + 1.97 = 1.97
0.95X + X2 = 1.97

The X term is 0.95X.  Take half its coefficient (0.475).
Square it (0.225625) and add it to both sides.

Add '0.225625' to each side of the equation.
0.95X + 0.225625 + X2 = 1.97 + 0.225625

Reorder the terms:
0.225625 + 0.95X + X2 = 1.97 + 0.225625

Combine like terms: 1.97 + 0.225625 = 2.195625
0.225625 + 0.95X + X2 = 2.195625

Factor a perfect square on the left side:
(X + 0.475)(X + 0.475) = 2.195625

Calculate the square root of the right side: 1.481764151

Break this problem into two subproblems by setting 
(X + 0.475) equal to 1.481764151 and -1.481764151.


Subproblem 1
X + 0.475 = 1.481764151

Simplifying
X + 0.475 = 1.481764151

Reorder the terms:
0.475 + X = 1.481764151

Solving
0.475 + X = 1.481764151

Solving for variable 'X'.

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

Add '-0.475' to each side of the equation.
0.475 + -0.475 + X = 1.481764151 + -0.475

Combine like terms: 0.475 + -0.475 = 0.000
0.000 + X = 1.481764151 + -0.475
X = 1.481764151 + -0.475

Combine like terms: 1.481764151 + -0.475 = 1.006764151
X = 1.006764151

Simplifying
X = 1.006764151


Subproblem 2
X + 0.475 = -1.481764151

Simplifying
X + 0.475 = -1.481764151

Reorder the terms:
0.475 + X = -1.481764151

Solving
0.475 + X = -1.481764151

Solving for variable 'X'.

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

Add '-0.475' to each side of the equation.
0.475 + -0.475 + X = -1.481764151 + -0.475

Combine like terms: 0.475 + -0.475 = 0.000
0.000 + X = -1.481764151 + -0.475
X = -1.481764151 + -0.475

Combine like terms: -1.481764151 + -0.475 = -1.956764151
X = -1.956764151

Simplifying
X = -1.956764151


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {1.006764151, -1.956764151}

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