9.8x^2-10x-50=0

Solution for 9.8x^2-10x-50=0 equation:

Simplifying
9.8x2 + -10x + -50 = 0

Reorder the terms:
-50 + -10x + 9.8x2 = 0

Solving
-50 + -10x + 9.8x2 = 0

Solving for variable 'x'.

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

Divide each side by '9.8'.
-5.102040816 + -1.020408163x + x2 = 0

Move the constant term to the right:

Add '5.102040816' to each side of the equation.
-5.102040816 + -1.020408163x + 5.102040816 + x2 = 0 + 5.102040816

Reorder the terms:
-5.102040816 + 5.102040816 + -1.020408163x + x2 = 0 + 5.102040816

Combine like terms: -5.102040816 + 5.102040816 = 0.000000000
0.000000000 + -1.020408163x + x2 = 0 + 5.102040816
-1.020408163x + x2 = 0 + 5.102040816

Combine like terms: 0 + 5.102040816 = 5.102040816
-1.020408163x + x2 = 5.102040816

The x term is -1.020408163x.  Take half its coefficient (-0.5102040815).
Square it (0.2603082048) and add it to both sides.

Add '0.2603082048' to each side of the equation.
-1.020408163x + 0.2603082048 + x2 = 5.102040816 + 0.2603082048

Reorder the terms:
0.2603082048 + -1.020408163x + x2 = 5.102040816 + 0.2603082048

Combine like terms: 5.102040816 + 0.2603082048 = 5.3623490208
0.2603082048 + -1.020408163x + x2 = 5.3623490208

Factor a perfect square on the left side:
(x + -0.5102040815)(x + -0.5102040815) = 5.3623490208

Calculate the square root of the right side: 2.315674636

Break this problem into two subproblems by setting 
(x + -0.5102040815) equal to 2.315674636 and -2.315674636.

Subproblem 1
x + -0.5102040815 = 2.315674636

Simplifying
x + -0.5102040815 = 2.315674636

Reorder the terms:
-0.5102040815 + x = 2.315674636

Solving
-0.5102040815 + x = 2.315674636

Solving for variable 'x'.

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

Add '0.5102040815' to each side of the equation.
-0.5102040815 + 0.5102040815 + x = 2.315674636 + 0.5102040815

Combine like terms: -0.5102040815 + 0.5102040815 = 0.0000000000
0.0000000000 + x = 2.315674636 + 0.5102040815
x = 2.315674636 + 0.5102040815

Combine like terms: 2.315674636 + 0.5102040815 = 2.8258787175
x = 2.8258787175

Simplifying
x = 2.8258787175

Subproblem 2
x + -0.5102040815 = -2.315674636

Simplifying
x + -0.5102040815 = -2.315674636

Reorder the terms:
-0.5102040815 + x = -2.315674636

Solving
-0.5102040815 + x = -2.315674636

Solving for variable 'x'.

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

Add '0.5102040815' to each side of the equation.
-0.5102040815 + 0.5102040815 + x = -2.315674636 + 0.5102040815

Combine like terms: -0.5102040815 + 0.5102040815 = 0.0000000000
0.0000000000 + x = -2.315674636 + 0.5102040815
x = -2.315674636 + 0.5102040815

Combine like terms: -2.315674636 + 0.5102040815 = -1.8054705545
x = -1.8054705545

Simplifying
x = -1.8054705545

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.8258787175, -1.8054705545}