2x^2+21x-2=0

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

Simplifying
2x2 + 21x + -2 = 0

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

Solving
-2 + 21x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
-1 + 10.5x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 10.5x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + 10.5x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 10.5x + x2 = 0 + 1
10.5x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
10.5x + x2 = 1

The x term is 10.5x.  Take half its coefficient (5.25).
Square it (27.5625) and add it to both sides.

Add '27.5625' to each side of the equation.
10.5x + 27.5625 + x2 = 1 + 27.5625

Reorder the terms:
27.5625 + 10.5x + x2 = 1 + 27.5625

Combine like terms: 1 + 27.5625 = 28.5625
27.5625 + 10.5x + x2 = 28.5625

Factor a perfect square on the left side:
(x + 5.25)(x + 5.25) = 28.5625

Calculate the square root of the right side: 5.344389582

Break this problem into two subproblems by setting 
(x + 5.25) equal to 5.344389582 and -5.344389582.

Subproblem 1
x + 5.25 = 5.344389582

Simplifying
x + 5.25 = 5.344389582

Reorder the terms:
5.25 + x = 5.344389582

Solving
5.25 + x = 5.344389582

Solving for variable 'x'.

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

Add '-5.25' to each side of the equation.
5.25 + -5.25 + x = 5.344389582 + -5.25

Combine like terms: 5.25 + -5.25 = 0.00
0.00 + x = 5.344389582 + -5.25
x = 5.344389582 + -5.25

Combine like terms: 5.344389582 + -5.25 = 0.094389582
x = 0.094389582

Simplifying
x = 0.094389582

Subproblem 2
x + 5.25 = -5.344389582

Simplifying
x + 5.25 = -5.344389582

Reorder the terms:
5.25 + x = -5.344389582

Solving
5.25 + x = -5.344389582

Solving for variable 'x'.

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

Add '-5.25' to each side of the equation.
5.25 + -5.25 + x = -5.344389582 + -5.25

Combine like terms: 5.25 + -5.25 = 0.00
0.00 + x = -5.344389582 + -5.25
x = -5.344389582 + -5.25

Combine like terms: -5.344389582 + -5.25 = -10.594389582
x = -10.594389582

Simplifying
x = -10.594389582

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.094389582, -10.594389582}