-21x^2-57x-2=0

Solution for -21x^2-57x-2=0 equation:

Simplifying
-21x2 + -57x + -2 = 0

Reorder the terms:
-2 + -57x + -21x2 = 0

Solving
-2 + -57x + -21x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(2 + 57x + 21x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(2 + 57x + 21x2)' equal to zero and attempt to solve:

Simplifying
2 + 57x + 21x2 = 0

Solving
2 + 57x + 21x2 = 0

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

Divide each side by '21'.
0.09523809524 + 2.714285714x + x2 = 0

Move the constant term to the right:

Add '-0.09523809524' to each side of the equation.
0.09523809524 + 2.714285714x + -0.09523809524 + x2 = 0 + -0.09523809524

Reorder the terms:
0.09523809524 + -0.09523809524 + 2.714285714x + x2 = 0 + -0.09523809524

Combine like terms: 0.09523809524 + -0.09523809524 = 0.00000000000
0.00000000000 + 2.714285714x + x2 = 0 + -0.09523809524
2.714285714x + x2 = 0 + -0.09523809524

Combine like terms: 0 + -0.09523809524 = -0.09523809524
2.714285714x + x2 = -0.09523809524

The x term is 2.714285714x.  Take half its coefficient (1.357142857).
Square it (1.841836734) and add it to both sides.

Add '1.841836734' to each side of the equation.
2.714285714x + 1.841836734 + x2 = -0.09523809524 + 1.841836734

Reorder the terms:
1.841836734 + 2.714285714x + x2 = -0.09523809524 + 1.841836734

Combine like terms: -0.09523809524 + 1.841836734 = 1.74659863876
1.841836734 + 2.714285714x + x2 = 1.74659863876

Factor a perfect square on the left side:
(x + 1.357142857)(x + 1.357142857) = 1.74659863876

Calculate the square root of the right side: 1.321589437

Break this problem into two subproblems by setting 
(x + 1.357142857) equal to 1.321589437 and -1.321589437.

Subproblem 1
x + 1.357142857 = 1.321589437

Simplifying
x + 1.357142857 = 1.321589437

Reorder the terms:
1.357142857 + x = 1.321589437

Solving
1.357142857 + x = 1.321589437

Solving for variable 'x'.

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

Add '-1.357142857' to each side of the equation.
1.357142857 + -1.357142857 + x = 1.321589437 + -1.357142857

Combine like terms: 1.357142857 + -1.357142857 = 0.000000000
0.000000000 + x = 1.321589437 + -1.357142857
x = 1.321589437 + -1.357142857

Combine like terms: 1.321589437 + -1.357142857 = -0.03555342
x = -0.03555342

Simplifying
x = -0.03555342

Subproblem 2
x + 1.357142857 = -1.321589437

Simplifying
x + 1.357142857 = -1.321589437

Reorder the terms:
1.357142857 + x = -1.321589437

Solving
1.357142857 + x = -1.321589437

Solving for variable 'x'.

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

Add '-1.357142857' to each side of the equation.
1.357142857 + -1.357142857 + x = -1.321589437 + -1.357142857

Combine like terms: 1.357142857 + -1.357142857 = 0.000000000
0.000000000 + x = -1.321589437 + -1.357142857
x = -1.321589437 + -1.357142857

Combine like terms: -1.321589437 + -1.357142857 = -2.678732294
x = -2.678732294

Simplifying
x = -2.678732294

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.03555342, -2.678732294}
Solution
x = {-0.03555342, -2.678732294}