4.9x^2-50x-100=0

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Solution for 4.9x^2-50x-100=0 equation: 


Simplifying
4.9x2 + -50x + -100 = 0

Reorder the terms:
-100 + -50x + 4.9x2 = 0

Solving
-100 + -50x + 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'.
-20.40816327 + -10.20408163x + x2 = 0

Move the constant term to the right:

Add '20.40816327' to each side of the equation.
-20.40816327 + -10.20408163x + 20.40816327 + x2 = 0 + 20.40816327

Reorder the terms:
-20.40816327 + 20.40816327 + -10.20408163x + x2 = 0 + 20.40816327

Combine like terms: -20.40816327 + 20.40816327 = 0.00000000
0.00000000 + -10.20408163x + x2 = 0 + 20.40816327
-10.20408163x + x2 = 0 + 20.40816327

Combine like terms: 0 + 20.40816327 = 20.40816327
-10.20408163x + x2 = 20.40816327

The x term is -10.20408163x.  Take half its coefficient (-5.102040815).
Square it (26.03082048) and add it to both sides.

Add '26.03082048' to each side of the equation.
-10.20408163x + 26.03082048 + x2 = 20.40816327 + 26.03082048

Reorder the terms:
26.03082048 + -10.20408163x + x2 = 20.40816327 + 26.03082048

Combine like terms: 20.40816327 + 26.03082048 = 46.43898375
26.03082048 + -10.20408163x + x2 = 46.43898375

Factor a perfect square on the left side:
(x + -5.102040815)(x + -5.102040815) = 46.43898375

Calculate the square root of the right side: 6.814615451

Break this problem into two subproblems by setting 
(x + -5.102040815) equal to 6.814615451 and -6.814615451.


Subproblem 1
x + -5.102040815 = 6.814615451

Simplifying
x + -5.102040815 = 6.814615451

Reorder the terms:
-5.102040815 + x = 6.814615451

Solving
-5.102040815 + x = 6.814615451

Solving for variable 'x'.

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

Add '5.102040815' to each side of the equation.
-5.102040815 + 5.102040815 + x = 6.814615451 + 5.102040815

Combine like terms: -5.102040815 + 5.102040815 = 0.000000000
0.000000000 + x = 6.814615451 + 5.102040815
x = 6.814615451 + 5.102040815

Combine like terms: 6.814615451 + 5.102040815 = 11.916656266
x = 11.916656266

Simplifying
x = 11.916656266


Subproblem 2
x + -5.102040815 = -6.814615451

Simplifying
x + -5.102040815 = -6.814615451

Reorder the terms:
-5.102040815 + x = -6.814615451

Solving
-5.102040815 + x = -6.814615451

Solving for variable 'x'.

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

Add '5.102040815' to each side of the equation.
-5.102040815 + 5.102040815 + x = -6.814615451 + 5.102040815

Combine like terms: -5.102040815 + 5.102040815 = 0.000000000
0.000000000 + x = -6.814615451 + 5.102040815
x = -6.814615451 + 5.102040815

Combine like terms: -6.814615451 + 5.102040815 = -1.712574636
x = -1.712574636

Simplifying
x = -1.712574636


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.916656266, -1.712574636}

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