4.9X^2+38.5X+5.6=0

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Solution for 4.9X^2+38.5X+5.6=0 equation: 


Simplifying
4.9X2 + 38.5X + 5.6 = 0

Reorder the terms:
5.6 + 38.5X + 4.9X2 = 0

Solving
5.6 + 38.5X + 4.9X2 = 0

Solving for variable 'X'.

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

Divide each side by '4.9'.
1.142857143 + 7.857142857X + X2 = 0

Move the constant term to the right:

Add '-1.142857143' to each side of the equation.
1.142857143 + 7.857142857X + -1.142857143 + X2 = 0 + -1.142857143

Reorder the terms:
1.142857143 + -1.142857143 + 7.857142857X + X2 = 0 + -1.142857143

Combine like terms: 1.142857143 + -1.142857143 = 0.000000000
0.000000000 + 7.857142857X + X2 = 0 + -1.142857143
7.857142857X + X2 = 0 + -1.142857143

Combine like terms: 0 + -1.142857143 = -1.142857143
7.857142857X + X2 = -1.142857143

The X term is 7.857142857X.  Take half its coefficient (3.928571429).
Square it (15.43367347) and add it to both sides.

Add '15.43367347' to each side of the equation.
7.857142857X + 15.43367347 + X2 = -1.142857143 + 15.43367347

Reorder the terms:
15.43367347 + 7.857142857X + X2 = -1.142857143 + 15.43367347

Combine like terms: -1.142857143 + 15.43367347 = 14.290816327
15.43367347 + 7.857142857X + X2 = 14.290816327

Factor a perfect square on the left side:
(X + 3.928571429)(X + 3.928571429) = 14.290816327

Calculate the square root of the right side: 3.780319606

Break this problem into two subproblems by setting 
(X + 3.928571429) equal to 3.780319606 and -3.780319606.


Subproblem 1
X + 3.928571429 = 3.780319606

Simplifying
X + 3.928571429 = 3.780319606

Reorder the terms:
3.928571429 + X = 3.780319606

Solving
3.928571429 + X = 3.780319606

Solving for variable 'X'.

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

Add '-3.928571429' to each side of the equation.
3.928571429 + -3.928571429 + X = 3.780319606 + -3.928571429

Combine like terms: 3.928571429 + -3.928571429 = 0.000000000
0.000000000 + X = 3.780319606 + -3.928571429
X = 3.780319606 + -3.928571429

Combine like terms: 3.780319606 + -3.928571429 = -0.148251823
X = -0.148251823

Simplifying
X = -0.148251823


Subproblem 2
X + 3.928571429 = -3.780319606

Simplifying
X + 3.928571429 = -3.780319606

Reorder the terms:
3.928571429 + X = -3.780319606

Solving
3.928571429 + X = -3.780319606

Solving for variable 'X'.

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

Add '-3.928571429' to each side of the equation.
3.928571429 + -3.928571429 + X = -3.780319606 + -3.928571429

Combine like terms: 3.928571429 + -3.928571429 = 0.000000000
0.000000000 + X = -3.780319606 + -3.928571429
X = -3.780319606 + -3.928571429

Combine like terms: -3.780319606 + -3.928571429 = -7.708891035
X = -7.708891035

Simplifying
X = -7.708891035


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {-0.148251823, -7.708891035}

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