9x^2+21x-2=0

Solution for 9x^2+21x-2=0 equation:

Simplifying
9x2 + 21x + -2 = 0

Reorder the terms:
-2 + 21x + 9x2 = 0

Solving
-2 + 21x + 9x2 = 0

Solving for variable 'x'.

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

Divide each side by '9'.
-0.2222222222 + 2.333333333x + x2 = 0

Move the constant term to the right:

Add '0.2222222222' to each side of the equation.
-0.2222222222 + 2.333333333x + 0.2222222222 + x2 = 0 + 0.2222222222

Reorder the terms:
-0.2222222222 + 0.2222222222 + 2.333333333x + x2 = 0 + 0.2222222222

Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000
0.0000000000 + 2.333333333x + x2 = 0 + 0.2222222222
2.333333333x + x2 = 0 + 0.2222222222

Combine like terms: 0 + 0.2222222222 = 0.2222222222
2.333333333x + x2 = 0.2222222222

The x term is 2.333333333x.  Take half its coefficient (1.166666667).
Square it (1.361111112) and add it to both sides.

Add '1.361111112' to each side of the equation.
2.333333333x + 1.361111112 + x2 = 0.2222222222 + 1.361111112

Reorder the terms:
1.361111112 + 2.333333333x + x2 = 0.2222222222 + 1.361111112

Combine like terms: 0.2222222222 + 1.361111112 = 1.5833333342
1.361111112 + 2.333333333x + x2 = 1.5833333342

Factor a perfect square on the left side:
(x + 1.166666667)(x + 1.166666667) = 1.5833333342

Calculate the square root of the right side: 1.25830574

Break this problem into two subproblems by setting 
(x + 1.166666667) equal to 1.25830574 and -1.25830574.

Subproblem 1
x + 1.166666667 = 1.25830574

Simplifying
x + 1.166666667 = 1.25830574

Reorder the terms:
1.166666667 + x = 1.25830574

Solving
1.166666667 + x = 1.25830574

Solving for variable 'x'.

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

Add '-1.166666667' to each side of the equation.
1.166666667 + -1.166666667 + x = 1.25830574 + -1.166666667

Combine like terms: 1.166666667 + -1.166666667 = 0.000000000
0.000000000 + x = 1.25830574 + -1.166666667
x = 1.25830574 + -1.166666667

Combine like terms: 1.25830574 + -1.166666667 = 0.091639073
x = 0.091639073

Simplifying
x = 0.091639073

Subproblem 2
x + 1.166666667 = -1.25830574

Simplifying
x + 1.166666667 = -1.25830574

Reorder the terms:
1.166666667 + x = -1.25830574

Solving
1.166666667 + x = -1.25830574

Solving for variable 'x'.

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

Add '-1.166666667' to each side of the equation.
1.166666667 + -1.166666667 + x = -1.25830574 + -1.166666667

Combine like terms: 1.166666667 + -1.166666667 = 0.000000000
0.000000000 + x = -1.25830574 + -1.166666667
x = -1.25830574 + -1.166666667

Combine like terms: -1.25830574 + -1.166666667 = -2.424972407
x = -2.424972407

Simplifying
x = -2.424972407

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.091639073, -2.424972407}