10a^2-20a+9=3

Solution for 10a^2-20a+9=3 equation:

Simplifying
10a2 + -20a + 9 = 3

Reorder the terms:
9 + -20a + 10a2 = 3

Solving
9 + -20a + 10a2 = 3

Solving for variable 'a'.

Reorder the terms:
9 + -3 + -20a + 10a2 = 3 + -3

Combine like terms: 9 + -3 = 6
6 + -20a + 10a2 = 3 + -3

Combine like terms: 3 + -3 = 0
6 + -20a + 10a2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -10a + 5a2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + -10a + 5a2)' equal to zero and attempt to solve:

Simplifying
3 + -10a + 5a2 = 0

Solving
3 + -10a + 5a2 = 0

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

Divide each side by '5'.
0.6 + -2a + a2 = 0

Move the constant term to the right:

Add '-0.6' to each side of the equation.
0.6 + -2a + -0.6 + a2 = 0 + -0.6

Reorder the terms:
0.6 + -0.6 + -2a + a2 = 0 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + -2a + a2 = 0 + -0.6
-2a + a2 = 0 + -0.6

Combine like terms: 0 + -0.6 = -0.6
-2a + a2 = -0.6

The a term is -2a.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2a + 1 + a2 = -0.6 + 1

Reorder the terms:
1 + -2a + a2 = -0.6 + 1

Combine like terms: -0.6 + 1 = 0.4
1 + -2a + a2 = 0.4

Factor a perfect square on the left side:
(a + -1)(a + -1) = 0.4

Calculate the square root of the right side: 0.632455532

Break this problem into two subproblems by setting 
(a + -1) equal to 0.632455532 and -0.632455532.

Subproblem 1
a + -1 = 0.632455532

Simplifying
a + -1 = 0.632455532

Reorder the terms:
-1 + a = 0.632455532

Solving
-1 + a = 0.632455532

Solving for variable 'a'.

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

Add '1' to each side of the equation.
-1 + 1 + a = 0.632455532 + 1

Combine like terms: -1 + 1 = 0
0 + a = 0.632455532 + 1
a = 0.632455532 + 1

Combine like terms: 0.632455532 + 1 = 1.632455532
a = 1.632455532

Simplifying
a = 1.632455532

Subproblem 2
a + -1 = -0.632455532

Simplifying
a + -1 = -0.632455532

Reorder the terms:
-1 + a = -0.632455532

Solving
-1 + a = -0.632455532

Solving for variable 'a'.

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

Add '1' to each side of the equation.
-1 + 1 + a = -0.632455532 + 1

Combine like terms: -1 + 1 = 0
0 + a = -0.632455532 + 1
a = -0.632455532 + 1

Combine like terms: -0.632455532 + 1 = 0.367544468
a = 0.367544468

Simplifying
a = 0.367544468

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {1.632455532, 0.367544468}
Solution
a = {1.632455532, 0.367544468}