10a^2+20a+100=96

Solution for 10a^2+20a+100=96 equation:

Simplifying
10a2 + 20a + 100 = 96

Reorder the terms:
100 + 20a + 10a2 = 96

Solving
100 + 20a + 10a2 = 96

Solving for variable 'a'.

Reorder the terms:
100 + -96 + 20a + 10a2 = 96 + -96

Combine like terms: 100 + -96 = 4
4 + 20a + 10a2 = 96 + -96

Combine like terms: 96 + -96 = 0
4 + 20a + 10a2 = 0

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

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

Simplifying
2 + 10a + 5a2 = 0

Solving
2 + 10a + 5a2 = 0

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

Divide each side by '5'.
0.4 + 2a + a2 = 0

Move the constant term to the right:

Add '-0.4' to each side of the equation.
0.4 + 2a + -0.4 + a2 = 0 + -0.4

Reorder the terms:
0.4 + -0.4 + 2a + a2 = 0 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + 2a + a2 = 0 + -0.4
2a + a2 = 0 + -0.4

Combine like terms: 0 + -0.4 = -0.4
2a + a2 = -0.4

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 = -0.4 + 1

Reorder the terms:
1 + 2a + a2 = -0.4 + 1

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

Factor a perfect square on the left side:
(a + 1)(a + 1) = 0.6

Calculate the square root of the right side: 0.774596669

Break this problem into two subproblems by setting 
(a + 1) equal to 0.774596669 and -0.774596669.

Subproblem 1
a + 1 = 0.774596669

Simplifying
a + 1 = 0.774596669

Reorder the terms:
1 + a = 0.774596669

Solving
1 + a = 0.774596669

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 = 0.774596669 + -1

Combine like terms: 1 + -1 = 0
0 + a = 0.774596669 + -1
a = 0.774596669 + -1

Combine like terms: 0.774596669 + -1 = -0.225403331
a = -0.225403331

Simplifying
a = -0.225403331

Subproblem 2
a + 1 = -0.774596669

Simplifying
a + 1 = -0.774596669

Reorder the terms:
1 + a = -0.774596669

Solving
1 + a = -0.774596669

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 = -0.774596669 + -1

Combine like terms: 1 + -1 = 0
0 + a = -0.774596669 + -1
a = -0.774596669 + -1

Combine like terms: -0.774596669 + -1 = -1.774596669
a = -1.774596669

Simplifying
a = -1.774596669

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {-0.225403331, -1.774596669}
Solution
a = {-0.225403331, -1.774596669}