5.02x^2-4.19x-2.057=0

Solution for 5.02x^2-4.19x-2.057=0 equation:

Simplifying
5.02x2 + -4.19x + -2.057 = 0

Reorder the terms:
-2.057 + -4.19x + 5.02x2 = 0

Solving
-2.057 + -4.19x + 5.02x2 = 0

Solving for variable 'x'.

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

Divide each side by '5.02'.
-0.4097609562 + -0.8346613546x + x2 = 0

Move the constant term to the right:

Add '0.4097609562' to each side of the equation.
-0.4097609562 + -0.8346613546x + 0.4097609562 + x2 = 0 + 0.4097609562

Reorder the terms:
-0.4097609562 + 0.4097609562 + -0.8346613546x + x2 = 0 + 0.4097609562

Combine like terms: -0.4097609562 + 0.4097609562 = 0.0000000000
0.0000000000 + -0.8346613546x + x2 = 0 + 0.4097609562
-0.8346613546x + x2 = 0 + 0.4097609562

Combine like terms: 0 + 0.4097609562 = 0.4097609562
-0.8346613546x + x2 = 0.4097609562

The x term is -0.8346613546x.  Take half its coefficient (-0.4173306773).
Square it (0.1741648942) and add it to both sides.

Add '0.1741648942' to each side of the equation.
-0.8346613546x + 0.1741648942 + x2 = 0.4097609562 + 0.1741648942

Reorder the terms:
0.1741648942 + -0.8346613546x + x2 = 0.4097609562 + 0.1741648942

Combine like terms: 0.4097609562 + 0.1741648942 = 0.5839258504
0.1741648942 + -0.8346613546x + x2 = 0.5839258504

Factor a perfect square on the left side:
(x + -0.4173306773)(x + -0.4173306773) = 0.5839258504

Calculate the square root of the right side: 0.764150411

Break this problem into two subproblems by setting 
(x + -0.4173306773) equal to 0.764150411 and -0.764150411.

Subproblem 1
x + -0.4173306773 = 0.764150411

Simplifying
x + -0.4173306773 = 0.764150411

Reorder the terms:
-0.4173306773 + x = 0.764150411

Solving
-0.4173306773 + x = 0.764150411

Solving for variable 'x'.

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

Add '0.4173306773' to each side of the equation.
-0.4173306773 + 0.4173306773 + x = 0.764150411 + 0.4173306773

Combine like terms: -0.4173306773 + 0.4173306773 = 0.0000000000
0.0000000000 + x = 0.764150411 + 0.4173306773
x = 0.764150411 + 0.4173306773

Combine like terms: 0.764150411 + 0.4173306773 = 1.1814810883
x = 1.1814810883

Simplifying
x = 1.1814810883

Subproblem 2
x + -0.4173306773 = -0.764150411

Simplifying
x + -0.4173306773 = -0.764150411

Reorder the terms:
-0.4173306773 + x = -0.764150411

Solving
-0.4173306773 + x = -0.764150411

Solving for variable 'x'.

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

Add '0.4173306773' to each side of the equation.
-0.4173306773 + 0.4173306773 + x = -0.764150411 + 0.4173306773

Combine like terms: -0.4173306773 + 0.4173306773 = 0.0000000000
0.0000000000 + x = -0.764150411 + 0.4173306773
x = -0.764150411 + 0.4173306773

Combine like terms: -0.764150411 + 0.4173306773 = -0.3468197337
x = -0.3468197337

Simplifying
x = -0.3468197337

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.1814810883, -0.3468197337}