18x^2+20x=-11x+4

Solution for 18x^2+20x=-11x+4 equation:

Simplifying
18x2 + 20x = -11x + 4

Reorder the terms:
20x + 18x2 = -11x + 4

Reorder the terms:
20x + 18x2 = 4 + -11x

Solving
20x + 18x2 = 4 + -11x

Solving for variable 'x'.

Reorder the terms:
-4 + 20x + 11x + 18x2 = 4 + -11x + -4 + 11x

Combine like terms: 20x + 11x = 31x
-4 + 31x + 18x2 = 4 + -11x + -4 + 11x

Reorder the terms:
-4 + 31x + 18x2 = 4 + -4 + -11x + 11x

Combine like terms: 4 + -4 = 0
-4 + 31x + 18x2 = 0 + -11x + 11x
-4 + 31x + 18x2 = -11x + 11x

Combine like terms: -11x + 11x = 0
-4 + 31x + 18x2 = 0

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

Divide each side by '18'.
-0.2222222222 + 1.722222222x + x2 = 0

Move the constant term to the right:

Add '0.2222222222' to each side of the equation.
-0.2222222222 + 1.722222222x + 0.2222222222 + x2 = 0 + 0.2222222222

Reorder the terms:
-0.2222222222 + 0.2222222222 + 1.722222222x + x2 = 0 + 0.2222222222

Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000
0.0000000000 + 1.722222222x + x2 = 0 + 0.2222222222
1.722222222x + x2 = 0 + 0.2222222222

Combine like terms: 0 + 0.2222222222 = 0.2222222222
1.722222222x + x2 = 0.2222222222

The x term is 1.722222222x.  Take half its coefficient (0.861111111).
Square it (0.7415123455) and add it to both sides.

Add '0.7415123455' to each side of the equation.
1.722222222x + 0.7415123455 + x2 = 0.2222222222 + 0.7415123455

Reorder the terms:
0.7415123455 + 1.722222222x + x2 = 0.2222222222 + 0.7415123455

Combine like terms: 0.2222222222 + 0.7415123455 = 0.9637345677
0.7415123455 + 1.722222222x + x2 = 0.9637345677

Factor a perfect square on the left side:
(x + 0.861111111)(x + 0.861111111) = 0.9637345677

Calculate the square root of the right side: 0.981699836

Break this problem into two subproblems by setting 
(x + 0.861111111) equal to 0.981699836 and -0.981699836.

Subproblem 1
x + 0.861111111 = 0.981699836

Simplifying
x + 0.861111111 = 0.981699836

Reorder the terms:
0.861111111 + x = 0.981699836

Solving
0.861111111 + x = 0.981699836

Solving for variable 'x'.

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

Add '-0.861111111' to each side of the equation.
0.861111111 + -0.861111111 + x = 0.981699836 + -0.861111111

Combine like terms: 0.861111111 + -0.861111111 = 0.000000000
0.000000000 + x = 0.981699836 + -0.861111111
x = 0.981699836 + -0.861111111

Combine like terms: 0.981699836 + -0.861111111 = 0.120588725
x = 0.120588725

Simplifying
x = 0.120588725

Subproblem 2
x + 0.861111111 = -0.981699836

Simplifying
x + 0.861111111 = -0.981699836

Reorder the terms:
0.861111111 + x = -0.981699836

Solving
0.861111111 + x = -0.981699836

Solving for variable 'x'.

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

Add '-0.861111111' to each side of the equation.
0.861111111 + -0.861111111 + x = -0.981699836 + -0.861111111

Combine like terms: 0.861111111 + -0.861111111 = 0.000000000
0.000000000 + x = -0.981699836 + -0.861111111
x = -0.981699836 + -0.861111111

Combine like terms: -0.981699836 + -0.861111111 = -1.842810947
x = -1.842810947

Simplifying
x = -1.842810947

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.120588725, -1.842810947}