-2x^2-18x-21=0

Solution for -2x^2-18x-21=0 equation:

Simplifying
-2x2 + -18x + -21 = 0

Reorder the terms:
-21 + -18x + -2x2 = 0

Solving
-21 + -18x + -2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(21 + 18x + 2x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(21 + 18x + 2x2)' equal to zero and attempt to solve:

Simplifying
21 + 18x + 2x2 = 0

Solving
21 + 18x + 2x2 = 0

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

Divide each side by '2'.
10.5 + 9x + x2 = 0

Move the constant term to the right:

Add '-10.5' to each side of the equation.
10.5 + 9x + -10.5 + x2 = 0 + -10.5

Reorder the terms:
10.5 + -10.5 + 9x + x2 = 0 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + 9x + x2 = 0 + -10.5
9x + x2 = 0 + -10.5

Combine like terms: 0 + -10.5 = -10.5
9x + x2 = -10.5

The x term is 9x.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9x + 20.25 + x2 = -10.5 + 20.25

Reorder the terms:
20.25 + 9x + x2 = -10.5 + 20.25

Combine like terms: -10.5 + 20.25 = 9.75
20.25 + 9x + x2 = 9.75

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 9.75

Calculate the square root of the right side: 3.122498999

Break this problem into two subproblems by setting 
(x + 4.5) equal to 3.122498999 and -3.122498999.

Subproblem 1
x + 4.5 = 3.122498999

Simplifying
x + 4.5 = 3.122498999

Reorder the terms:
4.5 + x = 3.122498999

Solving
4.5 + x = 3.122498999

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = 3.122498999 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = 3.122498999 + -4.5
x = 3.122498999 + -4.5

Combine like terms: 3.122498999 + -4.5 = -1.377501001
x = -1.377501001

Simplifying
x = -1.377501001

Subproblem 2
x + 4.5 = -3.122498999

Simplifying
x + 4.5 = -3.122498999

Reorder the terms:
4.5 + x = -3.122498999

Solving
4.5 + x = -3.122498999

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = -3.122498999 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = -3.122498999 + -4.5
x = -3.122498999 + -4.5

Combine like terms: -3.122498999 + -4.5 = -7.622498999
x = -7.622498999

Simplifying
x = -7.622498999

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.377501001, -7.622498999}
Solution
x = {-1.377501001, -7.622498999}