22x^2+8x+4=840

Solution for 22x^2+8x+4=840 equation:

Simplifying
22x2 + 8x + 4 = 840

Reorder the terms:
4 + 8x + 22x2 = 840

Solving
4 + 8x + 22x2 = 840

Solving for variable 'x'.

Reorder the terms:
4 + -840 + 8x + 22x2 = 840 + -840

Combine like terms: 4 + -840 = -836
-836 + 8x + 22x2 = 840 + -840

Combine like terms: 840 + -840 = 0
-836 + 8x + 22x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-418 + 4x + 11x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-418 + 4x + 11x2)' equal to zero and attempt to solve:

Simplifying
-418 + 4x + 11x2 = 0

Solving
-418 + 4x + 11x2 = 0

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

Divide each side by '11'.
-38 + 0.3636363636x + x2 = 0

Move the constant term to the right:

Add '38' to each side of the equation.
-38 + 0.3636363636x + 38 + x2 = 0 + 38

Reorder the terms:
-38 + 38 + 0.3636363636x + x2 = 0 + 38

Combine like terms: -38 + 38 = 0
0 + 0.3636363636x + x2 = 0 + 38
0.3636363636x + x2 = 0 + 38

Combine like terms: 0 + 38 = 38
0.3636363636x + x2 = 38

The x term is 0.3636363636x.  Take half its coefficient (0.1818181818).
Square it (0.03305785123) and add it to both sides.

Add '0.03305785123' to each side of the equation.
0.3636363636x + 0.03305785123 + x2 = 38 + 0.03305785123

Reorder the terms:
0.03305785123 + 0.3636363636x + x2 = 38 + 0.03305785123

Combine like terms: 38 + 0.03305785123 = 38.03305785123
0.03305785123 + 0.3636363636x + x2 = 38.03305785123

Factor a perfect square on the left side:
(x + 0.1818181818)(x + 0.1818181818) = 38.03305785123

Calculate the square root of the right side: 6.167094766

Break this problem into two subproblems by setting 
(x + 0.1818181818) equal to 6.167094766 and -6.167094766.

Subproblem 1
x + 0.1818181818 = 6.167094766

Simplifying
x + 0.1818181818 = 6.167094766

Reorder the terms:
0.1818181818 + x = 6.167094766

Solving
0.1818181818 + x = 6.167094766

Solving for variable 'x'.

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

Add '-0.1818181818' to each side of the equation.
0.1818181818 + -0.1818181818 + x = 6.167094766 + -0.1818181818

Combine like terms: 0.1818181818 + -0.1818181818 = 0.0000000000
0.0000000000 + x = 6.167094766 + -0.1818181818
x = 6.167094766 + -0.1818181818

Combine like terms: 6.167094766 + -0.1818181818 = 5.9852765842
x = 5.9852765842

Simplifying
x = 5.9852765842

Subproblem 2
x + 0.1818181818 = -6.167094766

Simplifying
x + 0.1818181818 = -6.167094766

Reorder the terms:
0.1818181818 + x = -6.167094766

Solving
0.1818181818 + x = -6.167094766

Solving for variable 'x'.

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

Add '-0.1818181818' to each side of the equation.
0.1818181818 + -0.1818181818 + x = -6.167094766 + -0.1818181818

Combine like terms: 0.1818181818 + -0.1818181818 = 0.0000000000
0.0000000000 + x = -6.167094766 + -0.1818181818
x = -6.167094766 + -0.1818181818

Combine like terms: -6.167094766 + -0.1818181818 = -6.3489129478
x = -6.3489129478

Simplifying
x = -6.3489129478

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.9852765842, -6.3489129478}
Solution
x = {5.9852765842, -6.3489129478}