4x^2-2x-50=0

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

Simplifying
4x2 + -2x + -50 = 0

Reorder the terms:
-50 + -2x + 4x2 = 0

Solving
-50 + -2x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-25 + -1x + 2x2) = 0

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

Simplifying
-25 + -1x + 2x2 = 0

Solving
-25 + -1x + 2x2 = 0

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

Divide each side by '2'.
-12.5 + -0.5x + x2 = 0

Move the constant term to the right:

Add '12.5' to each side of the equation.
-12.5 + -0.5x + 12.5 + x2 = 0 + 12.5

Reorder the terms:
-12.5 + 12.5 + -0.5x + x2 = 0 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + -0.5x + x2 = 0 + 12.5
-0.5x + x2 = 0 + 12.5

Combine like terms: 0 + 12.5 = 12.5
-0.5x + x2 = 12.5

The x term is -0.5x.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5x + 0.0625 + x2 = 12.5 + 0.0625

Reorder the terms:
0.0625 + -0.5x + x2 = 12.5 + 0.0625

Combine like terms: 12.5 + 0.0625 = 12.5625
0.0625 + -0.5x + x2 = 12.5625

Factor a perfect square on the left side:
(x + -0.25)(x + -0.25) = 12.5625

Calculate the square root of the right side: 3.54436172

Break this problem into two subproblems by setting 
(x + -0.25) equal to 3.54436172 and -3.54436172.

Subproblem 1
x + -0.25 = 3.54436172

Simplifying
x + -0.25 = 3.54436172

Reorder the terms:
-0.25 + x = 3.54436172

Solving
-0.25 + x = 3.54436172

Solving for variable 'x'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + x = 3.54436172 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x = 3.54436172 + 0.25
x = 3.54436172 + 0.25

Combine like terms: 3.54436172 + 0.25 = 3.79436172
x = 3.79436172

Simplifying
x = 3.79436172

Subproblem 2
x + -0.25 = -3.54436172

Simplifying
x + -0.25 = -3.54436172

Reorder the terms:
-0.25 + x = -3.54436172

Solving
-0.25 + x = -3.54436172

Solving for variable 'x'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + x = -3.54436172 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x = -3.54436172 + 0.25
x = -3.54436172 + 0.25

Combine like terms: -3.54436172 + 0.25 = -3.29436172
x = -3.29436172

Simplifying
x = -3.29436172

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.79436172, -3.29436172}
Solution
x = {3.79436172, -3.29436172}