9x(-5-6x)-1.3=0

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Solution for 9x(-5-6x)-1.3=0 equation: 


Simplifying
9x(-5 + -6x) + -1.3 = 0
(-5 * 9x + -6x * 9x) + -1.3 = 0
(-45x + -54x2) + -1.3 = 0

Reorder the terms:
-1.3 + -45x + -54x2 = 0

Solving
-1.3 + -45x + -54x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-54 the coefficient of the squared term: 

Divide each side by '-54'.
0.02407407407 + 0.8333333333x + x2 = 0

Move the constant term to the right:

Add '-0.02407407407' to each side of the equation.
0.02407407407 + 0.8333333333x + -0.02407407407 + x2 = 0 + -0.02407407407

Reorder the terms:
0.02407407407 + -0.02407407407 + 0.8333333333x + x2 = 0 + -0.02407407407

Combine like terms: 0.02407407407 + -0.02407407407 = 0.00000000000
0.00000000000 + 0.8333333333x + x2 = 0 + -0.02407407407
0.8333333333x + x2 = 0 + -0.02407407407

Combine like terms: 0 + -0.02407407407 = -0.02407407407
0.8333333333x + x2 = -0.02407407407

The x term is 0.8333333333x.  Take half its coefficient (0.4166666667).
Square it (0.1736111111) and add it to both sides.

Add '0.1736111111' to each side of the equation.
0.8333333333x + 0.1736111111 + x2 = -0.02407407407 + 0.1736111111

Reorder the terms:
0.1736111111 + 0.8333333333x + x2 = -0.02407407407 + 0.1736111111

Combine like terms: -0.02407407407 + 0.1736111111 = 0.14953703703
0.1736111111 + 0.8333333333x + x2 = 0.14953703703

Factor a perfect square on the left side:
(x + 0.4166666667)(x + 0.4166666667) = 0.14953703703

Calculate the square root of the right side: 0.38670019

Break this problem into two subproblems by setting 
(x + 0.4166666667) equal to 0.38670019 and -0.38670019.


Subproblem 1
x + 0.4166666667 = 0.38670019

Simplifying
x + 0.4166666667 = 0.38670019

Reorder the terms:
0.4166666667 + x = 0.38670019

Solving
0.4166666667 + x = 0.38670019

Solving for variable 'x'.

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

Add '-0.4166666667' to each side of the equation.
0.4166666667 + -0.4166666667 + x = 0.38670019 + -0.4166666667

Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000
0.0000000000 + x = 0.38670019 + -0.4166666667
x = 0.38670019 + -0.4166666667

Combine like terms: 0.38670019 + -0.4166666667 = -0.0299664767
x = -0.0299664767

Simplifying
x = -0.0299664767


Subproblem 2
x + 0.4166666667 = -0.38670019

Simplifying
x + 0.4166666667 = -0.38670019

Reorder the terms:
0.4166666667 + x = -0.38670019

Solving
0.4166666667 + x = -0.38670019

Solving for variable 'x'.

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

Add '-0.4166666667' to each side of the equation.
0.4166666667 + -0.4166666667 + x = -0.38670019 + -0.4166666667

Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000
0.0000000000 + x = -0.38670019 + -0.4166666667
x = -0.38670019 + -0.4166666667

Combine like terms: -0.38670019 + -0.4166666667 = -0.8033668567
x = -0.8033668567

Simplifying
x = -0.8033668567


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.0299664767, -0.8033668567}

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