5x^2-55x-30=0

Solution for 5x^2-55x-30=0 equation:

Simplifying
5x2 + -55x + -30 = 0

Reorder the terms:
-30 + -55x + 5x2 = 0

Solving
-30 + -55x + 5x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-6 + -11x + x2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-6 + -11x + x2)' equal to zero and attempt to solve:

Simplifying
-6 + -11x + x2 = 0

Solving
-6 + -11x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + -11x + 6 + x2 = 0 + 6

Reorder the terms:
-6 + 6 + -11x + x2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -11x + x2 = 0 + 6
-11x + x2 = 0 + 6

Combine like terms: 0 + 6 = 6
-11x + x2 = 6

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 = 6 + 30.25

Reorder the terms:
30.25 + -11x + x2 = 6 + 30.25

Combine like terms: 6 + 30.25 = 36.25
30.25 + -11x + x2 = 36.25

Factor a perfect square on the left side:
(x + -5.5)(x + -5.5) = 36.25

Calculate the square root of the right side: 6.020797289

Break this problem into two subproblems by setting 
(x + -5.5) equal to 6.020797289 and -6.020797289.

Subproblem 1
x + -5.5 = 6.020797289

Simplifying
x + -5.5 = 6.020797289

Reorder the terms:
-5.5 + x = 6.020797289

Solving
-5.5 + x = 6.020797289

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 = 6.020797289 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + x = 6.020797289 + 5.5
x = 6.020797289 + 5.5

Combine like terms: 6.020797289 + 5.5 = 11.520797289
x = 11.520797289

Simplifying
x = 11.520797289

Subproblem 2
x + -5.5 = -6.020797289

Simplifying
x + -5.5 = -6.020797289

Reorder the terms:
-5.5 + x = -6.020797289

Solving
-5.5 + x = -6.020797289

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 = -6.020797289 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + x = -6.020797289 + 5.5
x = -6.020797289 + 5.5

Combine like terms: -6.020797289 + 5.5 = -0.520797289
x = -0.520797289

Simplifying
x = -0.520797289

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.520797289, -0.520797289}
Solution
x = {11.520797289, -0.520797289}