2x^2+22x-581670=0

Solution for 2x^2+22x-581670=0 equation:

Simplifying
2x2 + 22x + -581670 = 0

Reorder the terms:
-581670 + 22x + 2x2 = 0

Solving
-581670 + 22x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-290835 + 11x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-290835 + 11x + x2)' equal to zero and attempt to solve:

Simplifying
-290835 + 11x + x2 = 0

Solving
-290835 + 11x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '290835' to each side of the equation.
-290835 + 11x + 290835 + x2 = 0 + 290835

Reorder the terms:
-290835 + 290835 + 11x + x2 = 0 + 290835

Combine like terms: -290835 + 290835 = 0
0 + 11x + x2 = 0 + 290835
11x + x2 = 0 + 290835

Combine like terms: 0 + 290835 = 290835
11x + x2 = 290835

The x term is 11x.  Take half its coefficient (5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
11x + 30.25 + x2 = 290835 + 30.25

Reorder the terms:
30.25 + 11x + x2 = 290835 + 30.25

Combine like terms: 290835 + 30.25 = 290865.25
30.25 + 11x + x2 = 290865.25

Factor a perfect square on the left side:
(x + 5.5)(x + 5.5) = 290865.25

Calculate the square root of the right side: 539.319246829

Break this problem into two subproblems by setting 
(x + 5.5) equal to 539.319246829 and -539.319246829.

Subproblem 1
x + 5.5 = 539.319246829

Simplifying
x + 5.5 = 539.319246829

Reorder the terms:
5.5 + x = 539.319246829

Solving
5.5 + x = 539.319246829

Solving for variable 'x'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + x = 539.319246829 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x = 539.319246829 + -5.5
x = 539.319246829 + -5.5

Combine like terms: 539.319246829 + -5.5 = 533.819246829
x = 533.819246829

Simplifying
x = 533.819246829

Subproblem 2
x + 5.5 = -539.319246829

Simplifying
x + 5.5 = -539.319246829

Reorder the terms:
5.5 + x = -539.319246829

Solving
5.5 + x = -539.319246829

Solving for variable 'x'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + x = -539.319246829 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x = -539.319246829 + -5.5
x = -539.319246829 + -5.5

Combine like terms: -539.319246829 + -5.5 = -544.819246829
x = -544.819246829

Simplifying
x = -544.819246829

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {533.819246829, -544.819246829}
Solution
x = {533.819246829, -544.819246829}