-4.9x^2+30.5x+9.5=0

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Solution for -4.9x^2+30.5x+9.5=0 equation: 


Simplifying
-4.9x2 + 30.5x + 9.5 = 0

Reorder the terms:
9.5 + 30.5x + -4.9x2 = 0

Solving
9.5 + 30.5x + -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'.
-1.93877551 + -6.224489796x + x2 = 0

Move the constant term to the right:

Add '1.93877551' to each side of the equation.
-1.93877551 + -6.224489796x + 1.93877551 + x2 = 0 + 1.93877551

Reorder the terms:
-1.93877551 + 1.93877551 + -6.224489796x + x2 = 0 + 1.93877551

Combine like terms: -1.93877551 + 1.93877551 = 0.00000000
0.00000000 + -6.224489796x + x2 = 0 + 1.93877551
-6.224489796x + x2 = 0 + 1.93877551

Combine like terms: 0 + 1.93877551 = 1.93877551
-6.224489796x + x2 = 1.93877551

The x term is -6.224489796x.  Take half its coefficient (-3.112244898).
Square it (9.686068305) and add it to both sides.

Add '9.686068305' to each side of the equation.
-6.224489796x + 9.686068305 + x2 = 1.93877551 + 9.686068305

Reorder the terms:
9.686068305 + -6.224489796x + x2 = 1.93877551 + 9.686068305

Combine like terms: 1.93877551 + 9.686068305 = 11.624843815
9.686068305 + -6.224489796x + x2 = 11.624843815

Factor a perfect square on the left side:
(x + -3.112244898)(x + -3.112244898) = 11.624843815

Calculate the square root of the right side: 3.40952252

Break this problem into two subproblems by setting 
(x + -3.112244898) equal to 3.40952252 and -3.40952252.


Subproblem 1
x + -3.112244898 = 3.40952252

Simplifying
x + -3.112244898 = 3.40952252

Reorder the terms:
-3.112244898 + x = 3.40952252

Solving
-3.112244898 + x = 3.40952252

Solving for variable 'x'.

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

Add '3.112244898' to each side of the equation.
-3.112244898 + 3.112244898 + x = 3.40952252 + 3.112244898

Combine like terms: -3.112244898 + 3.112244898 = 0.000000000
0.000000000 + x = 3.40952252 + 3.112244898
x = 3.40952252 + 3.112244898

Combine like terms: 3.40952252 + 3.112244898 = 6.521767418
x = 6.521767418

Simplifying
x = 6.521767418


Subproblem 2
x + -3.112244898 = -3.40952252

Simplifying
x + -3.112244898 = -3.40952252

Reorder the terms:
-3.112244898 + x = -3.40952252

Solving
-3.112244898 + x = -3.40952252

Solving for variable 'x'.

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

Add '3.112244898' to each side of the equation.
-3.112244898 + 3.112244898 + x = -3.40952252 + 3.112244898

Combine like terms: -3.112244898 + 3.112244898 = 0.000000000
0.000000000 + x = -3.40952252 + 3.112244898
x = -3.40952252 + 3.112244898

Combine like terms: -3.40952252 + 3.112244898 = -0.297277622
x = -0.297277622

Simplifying
x = -0.297277622


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.521767418, -0.297277622}

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