-10a(9a-8)=1

Solution for -10a(9a-8)=1 equation:

Simplifying
-10a(9a + -8) = 1

Reorder the terms:
-10a(-8 + 9a) = 1
(-8 * -10a + 9a * -10a) = 1
(80a + -90a2) = 1

Solving
80a + -90a2 = 1

Solving for variable 'a'.

Reorder the terms:
-1 + 80a + -90a2 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + 80a + -90a2 = 0

Begin completing the square.  Divide all terms by
-90 the coefficient of the squared term: 

Divide each side by '-90'.
0.01111111111 + -0.8888888889a + a2 = 0.0

Move the constant term to the right:

Add '-0.01111111111' to each side of the equation.
0.01111111111 + -0.8888888889a + -0.01111111111 + a2 = 0.0 + -0.01111111111

Reorder the terms:
0.01111111111 + -0.01111111111 + -0.8888888889a + a2 = 0.0 + -0.01111111111

Combine like terms: 0.01111111111 + -0.01111111111 = 0.00000000000
0.00000000000 + -0.8888888889a + a2 = 0.0 + -0.01111111111
-0.8888888889a + a2 = 0.0 + -0.01111111111

Combine like terms: 0.0 + -0.01111111111 = -0.01111111111
-0.8888888889a + a2 = -0.01111111111

The a term is -0.8888888889a.  Take half its coefficient (-0.4444444445).
Square it (0.1975308642) and add it to both sides.

Add '0.1975308642' to each side of the equation.
-0.8888888889a + 0.1975308642 + a2 = -0.01111111111 + 0.1975308642

Reorder the terms:
0.1975308642 + -0.8888888889a + a2 = -0.01111111111 + 0.1975308642

Combine like terms: -0.01111111111 + 0.1975308642 = 0.18641975309
0.1975308642 + -0.8888888889a + a2 = 0.18641975309

Factor a perfect square on the left side:
(a + -0.4444444445)(a + -0.4444444445) = 0.18641975309

Calculate the square root of the right side: 0.431763538

Break this problem into two subproblems by setting 
(a + -0.4444444445) equal to 0.431763538 and -0.431763538.

Subproblem 1
a + -0.4444444445 = 0.431763538

Simplifying
a + -0.4444444445 = 0.431763538

Reorder the terms:
-0.4444444445 + a = 0.431763538

Solving
-0.4444444445 + a = 0.431763538

Solving for variable 'a'.

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

Add '0.4444444445' to each side of the equation.
-0.4444444445 + 0.4444444445 + a = 0.431763538 + 0.4444444445

Combine like terms: -0.4444444445 + 0.4444444445 = 0.0000000000
0.0000000000 + a = 0.431763538 + 0.4444444445
a = 0.431763538 + 0.4444444445

Combine like terms: 0.431763538 + 0.4444444445 = 0.8762079825
a = 0.8762079825

Simplifying
a = 0.8762079825

Subproblem 2
a + -0.4444444445 = -0.431763538

Simplifying
a + -0.4444444445 = -0.431763538

Reorder the terms:
-0.4444444445 + a = -0.431763538

Solving
-0.4444444445 + a = -0.431763538

Solving for variable 'a'.

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

Add '0.4444444445' to each side of the equation.
-0.4444444445 + 0.4444444445 + a = -0.431763538 + 0.4444444445

Combine like terms: -0.4444444445 + 0.4444444445 = 0.0000000000
0.0000000000 + a = -0.431763538 + 0.4444444445
a = -0.431763538 + 0.4444444445

Combine like terms: -0.431763538 + 0.4444444445 = 0.0126809065
a = 0.0126809065

Simplifying
a = 0.0126809065

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {0.8762079825, 0.0126809065}