50x^2-4x-764=0

Solution for 50x^2-4x-764=0 equation:

Simplifying
50x2 + -4x + -764 = 0

Reorder the terms:
-764 + -4x + 50x2 = 0

Solving
-764 + -4x + 50x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-382 + -2x + 25x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-382 + -2x + 25x2)' equal to zero and attempt to solve:

Simplifying
-382 + -2x + 25x2 = 0

Solving
-382 + -2x + 25x2 = 0

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

Divide each side by '25'.
-15.28 + -0.08x + x2 = 0

Move the constant term to the right:

Add '15.28' to each side of the equation.
-15.28 + -0.08x + 15.28 + x2 = 0 + 15.28

Reorder the terms:
-15.28 + 15.28 + -0.08x + x2 = 0 + 15.28

Combine like terms: -15.28 + 15.28 = 0.00
0.00 + -0.08x + x2 = 0 + 15.28
-0.08x + x2 = 0 + 15.28

Combine like terms: 0 + 15.28 = 15.28
-0.08x + x2 = 15.28

The x term is -0.08x.  Take half its coefficient (-0.04).
Square it (0.0016) and add it to both sides.

Add '0.0016' to each side of the equation.
-0.08x + 0.0016 + x2 = 15.28 + 0.0016

Reorder the terms:
0.0016 + -0.08x + x2 = 15.28 + 0.0016

Combine like terms: 15.28 + 0.0016 = 15.2816
0.0016 + -0.08x + x2 = 15.2816

Factor a perfect square on the left side:
(x + -0.04)(x + -0.04) = 15.2816

Calculate the square root of the right side: 3.90916871

Break this problem into two subproblems by setting 
(x + -0.04) equal to 3.90916871 and -3.90916871.

Subproblem 1
x + -0.04 = 3.90916871

Simplifying
x + -0.04 = 3.90916871

Reorder the terms:
-0.04 + x = 3.90916871

Solving
-0.04 + x = 3.90916871

Solving for variable 'x'.

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

Add '0.04' to each side of the equation.
-0.04 + 0.04 + x = 3.90916871 + 0.04

Combine like terms: -0.04 + 0.04 = 0.00
0.00 + x = 3.90916871 + 0.04
x = 3.90916871 + 0.04

Combine like terms: 3.90916871 + 0.04 = 3.94916871
x = 3.94916871

Simplifying
x = 3.94916871

Subproblem 2
x + -0.04 = -3.90916871

Simplifying
x + -0.04 = -3.90916871

Reorder the terms:
-0.04 + x = -3.90916871

Solving
-0.04 + x = -3.90916871

Solving for variable 'x'.

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

Add '0.04' to each side of the equation.
-0.04 + 0.04 + x = -3.90916871 + 0.04

Combine like terms: -0.04 + 0.04 = 0.00
0.00 + x = -3.90916871 + 0.04
x = -3.90916871 + 0.04

Combine like terms: -3.90916871 + 0.04 = -3.86916871
x = -3.86916871

Simplifying
x = -3.86916871

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.94916871, -3.86916871}
Solution
x = {3.94916871, -3.86916871}