308e^2+616e+308=1090

Solution for 308e^2+616e+308=1090 equation:

Simplifying
308e2 + 616e + 308 = 1090

Reorder the terms:
308 + 616e + 308e2 = 1090

Solving
308 + 616e + 308e2 = 1090

Solving for variable 'e'.

Reorder the terms:
308 + -1090 + 616e + 308e2 = 1090 + -1090

Combine like terms: 308 + -1090 = -782
-782 + 616e + 308e2 = 1090 + -1090

Combine like terms: 1090 + -1090 = 0
-782 + 616e + 308e2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-391 + 308e + 154e2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-391 + 308e + 154e2)' equal to zero and attempt to solve:

Simplifying
-391 + 308e + 154e2 = 0

Solving
-391 + 308e + 154e2 = 0

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

Divide each side by '154'.
-2.538961039 + 2e + e2 = 0

Move the constant term to the right:

Add '2.538961039' to each side of the equation.
-2.538961039 + 2e + 2.538961039 + e2 = 0 + 2.538961039

Reorder the terms:
-2.538961039 + 2.538961039 + 2e + e2 = 0 + 2.538961039

Combine like terms: -2.538961039 + 2.538961039 = 0.000000000
0.000000000 + 2e + e2 = 0 + 2.538961039
2e + e2 = 0 + 2.538961039

Combine like terms: 0 + 2.538961039 = 2.538961039
2e + e2 = 2.538961039

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

Add '1' to each side of the equation.
2e + 1 + e2 = 2.538961039 + 1

Reorder the terms:
1 + 2e + e2 = 2.538961039 + 1

Combine like terms: 2.538961039 + 1 = 3.538961039
1 + 2e + e2 = 3.538961039

Factor a perfect square on the left side:
(e + 1)(e + 1) = 3.538961039

Calculate the square root of the right side: 1.881212651

Break this problem into two subproblems by setting 
(e + 1) equal to 1.881212651 and -1.881212651.

Subproblem 1
e + 1 = 1.881212651

Simplifying
e + 1 = 1.881212651

Reorder the terms:
1 + e = 1.881212651

Solving
1 + e = 1.881212651

Solving for variable 'e'.

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

Add '-1' to each side of the equation.
1 + -1 + e = 1.881212651 + -1

Combine like terms: 1 + -1 = 0
0 + e = 1.881212651 + -1
e = 1.881212651 + -1

Combine like terms: 1.881212651 + -1 = 0.881212651
e = 0.881212651

Simplifying
e = 0.881212651

Subproblem 2
e + 1 = -1.881212651

Simplifying
e + 1 = -1.881212651

Reorder the terms:
1 + e = -1.881212651

Solving
1 + e = -1.881212651

Solving for variable 'e'.

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

Add '-1' to each side of the equation.
1 + -1 + e = -1.881212651 + -1

Combine like terms: 1 + -1 = 0
0 + e = -1.881212651 + -1
e = -1.881212651 + -1

Combine like terms: -1.881212651 + -1 = -2.881212651
e = -2.881212651

Simplifying
e = -2.881212651

Solution
The solution to the problem is based on the solutions
from the subproblems.
e = {0.881212651, -2.881212651}
Solution
e = {0.881212651, -2.881212651}