81x^2+20x-121=0

Solution for 81x^2+20x-121=0 equation:

Simplifying
81x2 + 20x + -121 = 0

Reorder the terms:
-121 + 20x + 81x2 = 0

Solving
-121 + 20x + 81x2 = 0

Solving for variable 'x'.

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

Divide each side by '81'.
-1.49382716 + 0.2469135802x + x2 = 0

Move the constant term to the right:

Add '1.49382716' to each side of the equation.
-1.49382716 + 0.2469135802x + 1.49382716 + x2 = 0 + 1.49382716

Reorder the terms:
-1.49382716 + 1.49382716 + 0.2469135802x + x2 = 0 + 1.49382716

Combine like terms: -1.49382716 + 1.49382716 = 0.00000000
0.00000000 + 0.2469135802x + x2 = 0 + 1.49382716
0.2469135802x + x2 = 0 + 1.49382716

Combine like terms: 0 + 1.49382716 = 1.49382716
0.2469135802x + x2 = 1.49382716

The x term is 0.2469135802x.  Take half its coefficient (0.1234567901).
Square it (0.01524157902) and add it to both sides.

Add '0.01524157902' to each side of the equation.
0.2469135802x + 0.01524157902 + x2 = 1.49382716 + 0.01524157902

Reorder the terms:
0.01524157902 + 0.2469135802x + x2 = 1.49382716 + 0.01524157902

Combine like terms: 1.49382716 + 0.01524157902 = 1.50906873902
0.01524157902 + 0.2469135802x + x2 = 1.50906873902

Factor a perfect square on the left side:
(x + 0.1234567901)(x + 0.1234567901) = 1.50906873902

Calculate the square root of the right side: 1.22844159

Break this problem into two subproblems by setting 
(x + 0.1234567901) equal to 1.22844159 and -1.22844159.

Subproblem 1
x + 0.1234567901 = 1.22844159

Simplifying
x + 0.1234567901 = 1.22844159

Reorder the terms:
0.1234567901 + x = 1.22844159

Solving
0.1234567901 + x = 1.22844159

Solving for variable 'x'.

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

Add '-0.1234567901' to each side of the equation.
0.1234567901 + -0.1234567901 + x = 1.22844159 + -0.1234567901

Combine like terms: 0.1234567901 + -0.1234567901 = 0.0000000000
0.0000000000 + x = 1.22844159 + -0.1234567901
x = 1.22844159 + -0.1234567901

Combine like terms: 1.22844159 + -0.1234567901 = 1.1049847999
x = 1.1049847999

Simplifying
x = 1.1049847999

Subproblem 2
x + 0.1234567901 = -1.22844159

Simplifying
x + 0.1234567901 = -1.22844159

Reorder the terms:
0.1234567901 + x = -1.22844159

Solving
0.1234567901 + x = -1.22844159

Solving for variable 'x'.

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

Add '-0.1234567901' to each side of the equation.
0.1234567901 + -0.1234567901 + x = -1.22844159 + -0.1234567901

Combine like terms: 0.1234567901 + -0.1234567901 = 0.0000000000
0.0000000000 + x = -1.22844159 + -0.1234567901
x = -1.22844159 + -0.1234567901

Combine like terms: -1.22844159 + -0.1234567901 = -1.3518983801
x = -1.3518983801

Simplifying
x = -1.3518983801

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.1049847999, -1.3518983801}