13x(5x-11)=-13

Solution for 13x(5x-11)=-13 equation:

Simplifying
13x(5x + -11) = -13

Reorder the terms:
13x(-11 + 5x) = -13
(-11 * 13x + 5x * 13x) = -13
(-143x + 65x2) = -13

Solving
-143x + 65x2 = -13

Solving for variable 'x'.

Reorder the terms:
13 + -143x + 65x2 = -13 + 13

Combine like terms: -13 + 13 = 0
13 + -143x + 65x2 = 0

Factor out the Greatest Common Factor (GCF), '13'.
13(1 + -11x + 5x2) = 0

Ignore the factor 13.
Subproblem 1
Set the factor '(1 + -11x + 5x2)' equal to zero and attempt to solve:

Simplifying
1 + -11x + 5x2 = 0

Solving
1 + -11x + 5x2 = 0

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

Divide each side by '5'.
0.2 + -2.2x + x2 = 0

Move the constant term to the right:

Add '-0.2' to each side of the equation.
0.2 + -2.2x + -0.2 + x2 = 0 + -0.2

Reorder the terms:
0.2 + -0.2 + -2.2x + x2 = 0 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + -2.2x + x2 = 0 + -0.2
-2.2x + x2 = 0 + -0.2

Combine like terms: 0 + -0.2 = -0.2
-2.2x + x2 = -0.2

The x term is -2.2x.  Take half its coefficient (-1.1).
Square it (1.21) and add it to both sides.

Add '1.21' to each side of the equation.
-2.2x + 1.21 + x2 = -0.2 + 1.21

Reorder the terms:
1.21 + -2.2x + x2 = -0.2 + 1.21

Combine like terms: -0.2 + 1.21 = 1.01
1.21 + -2.2x + x2 = 1.01

Factor a perfect square on the left side:
(x + -1.1)(x + -1.1) = 1.01

Calculate the square root of the right side: 1.004987562

Break this problem into two subproblems by setting 
(x + -1.1) equal to 1.004987562 and -1.004987562.

Subproblem 1
x + -1.1 = 1.004987562

Simplifying
x + -1.1 = 1.004987562

Reorder the terms:
-1.1 + x = 1.004987562

Solving
-1.1 + x = 1.004987562

Solving for variable 'x'.

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

Add '1.1' to each side of the equation.
-1.1 + 1.1 + x = 1.004987562 + 1.1

Combine like terms: -1.1 + 1.1 = 0.0
0.0 + x = 1.004987562 + 1.1
x = 1.004987562 + 1.1

Combine like terms: 1.004987562 + 1.1 = 2.104987562
x = 2.104987562

Simplifying
x = 2.104987562

Subproblem 2
x + -1.1 = -1.004987562

Simplifying
x + -1.1 = -1.004987562

Reorder the terms:
-1.1 + x = -1.004987562

Solving
-1.1 + x = -1.004987562

Solving for variable 'x'.

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

Add '1.1' to each side of the equation.
-1.1 + 1.1 + x = -1.004987562 + 1.1

Combine like terms: -1.1 + 1.1 = 0.0
0.0 + x = -1.004987562 + 1.1
x = -1.004987562 + 1.1

Combine like terms: -1.004987562 + 1.1 = 0.095012438
x = 0.095012438

Simplifying
x = 0.095012438

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.104987562, 0.095012438}
Solution
x = {2.104987562, 0.095012438}