11x^2+30x-171=0

Solution for 11x^2+30x-171=0 equation:

Simplifying
11x2 + 30x + -171 = 0

Reorder the terms:
-171 + 30x + 11x2 = 0

Solving
-171 + 30x + 11x2 = 0

Solving for variable 'x'.

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

Divide each side by '11'.
-15.54545455 + 2.727272727x + x2 = 0

Move the constant term to the right:

Add '15.54545455' to each side of the equation.
-15.54545455 + 2.727272727x + 15.54545455 + x2 = 0 + 15.54545455

Reorder the terms:
-15.54545455 + 15.54545455 + 2.727272727x + x2 = 0 + 15.54545455

Combine like terms: -15.54545455 + 15.54545455 = 0.00000000
0.00000000 + 2.727272727x + x2 = 0 + 15.54545455
2.727272727x + x2 = 0 + 15.54545455

Combine like terms: 0 + 15.54545455 = 15.54545455
2.727272727x + x2 = 15.54545455

The x term is 2.727272727x.  Take half its coefficient (1.363636364).
Square it (1.859504133) and add it to both sides.

Add '1.859504133' to each side of the equation.
2.727272727x + 1.859504133 + x2 = 15.54545455 + 1.859504133

Reorder the terms:
1.859504133 + 2.727272727x + x2 = 15.54545455 + 1.859504133

Combine like terms: 15.54545455 + 1.859504133 = 17.404958683
1.859504133 + 2.727272727x + x2 = 17.404958683

Factor a perfect square on the left side:
(x + 1.363636364)(x + 1.363636364) = 17.404958683

Calculate the square root of the right side: 4.171925057

Break this problem into two subproblems by setting 
(x + 1.363636364) equal to 4.171925057 and -4.171925057.

Subproblem 1
x + 1.363636364 = 4.171925057

Simplifying
x + 1.363636364 = 4.171925057

Reorder the terms:
1.363636364 + x = 4.171925057

Solving
1.363636364 + x = 4.171925057

Solving for variable 'x'.

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

Add '-1.363636364' to each side of the equation.
1.363636364 + -1.363636364 + x = 4.171925057 + -1.363636364

Combine like terms: 1.363636364 + -1.363636364 = 0.000000000
0.000000000 + x = 4.171925057 + -1.363636364
x = 4.171925057 + -1.363636364

Combine like terms: 4.171925057 + -1.363636364 = 2.808288693
x = 2.808288693

Simplifying
x = 2.808288693

Subproblem 2
x + 1.363636364 = -4.171925057

Simplifying
x + 1.363636364 = -4.171925057

Reorder the terms:
1.363636364 + x = -4.171925057

Solving
1.363636364 + x = -4.171925057

Solving for variable 'x'.

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

Add '-1.363636364' to each side of the equation.
1.363636364 + -1.363636364 + x = -4.171925057 + -1.363636364

Combine like terms: 1.363636364 + -1.363636364 = 0.000000000
0.000000000 + x = -4.171925057 + -1.363636364
x = -4.171925057 + -1.363636364

Combine like terms: -4.171925057 + -1.363636364 = -5.535561421
x = -5.535561421

Simplifying
x = -5.535561421

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.808288693, -5.535561421}