10a^2+12a=1

Solution for 10a^2+12a=1 equation:

Simplifying
10a2 + 12a = 1

Reorder the terms:
12a + 10a2 = 1

Solving
12a + 10a2 = 1

Solving for variable 'a'.

Reorder the terms:
-1 + 12a + 10a2 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + 12a + 10a2 = 0

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

Divide each side by '10'.
-0.1 + 1.2a + a2 = 0

Move the constant term to the right:

Add '0.1' to each side of the equation.
-0.1 + 1.2a + 0.1 + a2 = 0 + 0.1

Reorder the terms:
-0.1 + 0.1 + 1.2a + a2 = 0 + 0.1

Combine like terms: -0.1 + 0.1 = 0.0
0.0 + 1.2a + a2 = 0 + 0.1
1.2a + a2 = 0 + 0.1

Combine like terms: 0 + 0.1 = 0.1
1.2a + a2 = 0.1

The a term is 1.2a.  Take half its coefficient (0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
1.2a + 0.36 + a2 = 0.1 + 0.36

Reorder the terms:
0.36 + 1.2a + a2 = 0.1 + 0.36

Combine like terms: 0.1 + 0.36 = 0.46
0.36 + 1.2a + a2 = 0.46

Factor a perfect square on the left side:
(a + 0.6)(a + 0.6) = 0.46

Calculate the square root of the right side: 0.678232998

Break this problem into two subproblems by setting 
(a + 0.6) equal to 0.678232998 and -0.678232998.

Subproblem 1
a + 0.6 = 0.678232998

Simplifying
a + 0.6 = 0.678232998

Reorder the terms:
0.6 + a = 0.678232998

Solving
0.6 + a = 0.678232998

Solving for variable 'a'.

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

Add '-0.6' to each side of the equation.
0.6 + -0.6 + a = 0.678232998 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + a = 0.678232998 + -0.6
a = 0.678232998 + -0.6

Combine like terms: 0.678232998 + -0.6 = 0.078232998
a = 0.078232998

Simplifying
a = 0.078232998

Subproblem 2
a + 0.6 = -0.678232998

Simplifying
a + 0.6 = -0.678232998

Reorder the terms:
0.6 + a = -0.678232998

Solving
0.6 + a = -0.678232998

Solving for variable 'a'.

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

Add '-0.6' to each side of the equation.
0.6 + -0.6 + a = -0.678232998 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + a = -0.678232998 + -0.6
a = -0.678232998 + -0.6

Combine like terms: -0.678232998 + -0.6 = -1.278232998
a = -1.278232998

Simplifying
a = -1.278232998

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {0.078232998, -1.278232998}