-4.9x^2+38.5x+5.6=0

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 = 16.576530613
15.43367347 + -7.857142857x + x2 = 16.576530613

Factor a perfect square on the left side:
(x + -3.928571429)(x + -3.928571429) = 16.576530613

Calculate the square root of the right side: 4.071428572

Break this problem into two subproblems by setting 
(x + -3.928571429) equal to 4.071428572 and -4.071428572.

Subproblem 1
x + -3.928571429 = 4.071428572

Simplifying
x + -3.928571429 = 4.071428572

Reorder the terms:
-3.928571429 + x = 4.071428572

Solving
-3.928571429 + x = 4.071428572

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 = 4.071428572 + 3.928571429

Combine like terms: -3.928571429 + 3.928571429 = 0.000000000
0.000000000 + x = 4.071428572 + 3.928571429
x = 4.071428572 + 3.928571429

Combine like terms: 4.071428572 + 3.928571429 = 8.000000001
x = 8.000000001

Simplifying
x = 8.000000001

Subproblem 2
x + -3.928571429 = -4.071428572

Simplifying
x + -3.928571429 = -4.071428572

Reorder the terms:
-3.928571429 + x = -4.071428572

Solving
-3.928571429 + x = -4.071428572

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 = -4.071428572 + 3.928571429

Combine like terms: -3.928571429 + 3.928571429 = 0.000000000
0.000000000 + x = -4.071428572 + 3.928571429
x = -4.071428572 + 3.928571429

Combine like terms: -4.071428572 + 3.928571429 = -0.142857143
x = -0.142857143

Simplifying
x = -0.142857143

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.000000001, -0.142857143}