e^2+20e+10=0

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Solution for e^2+20e+10=0 equation: 


Simplifying
e2 + 20e + 10 = 0

Reorder the terms:
10 + 20e + e2 = 0

Solving
10 + 20e + e2 = 0

Solving for variable 'e'.

Begin completing the square.

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + 20e + -10 + e2 = 0 + -10

Reorder the terms:
10 + -10 + 20e + e2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + 20e + e2 = 0 + -10
20e + e2 = 0 + -10

Combine like terms: 0 + -10 = -10
20e + e2 = -10

The e term is 20e.  Take half its coefficient (10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
20e + 100 + e2 = -10 + 100

Reorder the terms:
100 + 20e + e2 = -10 + 100

Combine like terms: -10 + 100 = 90
100 + 20e + e2 = 90

Factor a perfect square on the left side:
(e + 10)(e + 10) = 90

Calculate the square root of the right side: 9.486832981

Break this problem into two subproblems by setting 
(e + 10) equal to 9.486832981 and -9.486832981.


Subproblem 1
e + 10 = 9.486832981

Simplifying
e + 10 = 9.486832981

Reorder the terms:
10 + e = 9.486832981

Solving
10 + e = 9.486832981

Solving for variable 'e'.

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

Add '-10' to each side of the equation.
10 + -10 + e = 9.486832981 + -10

Combine like terms: 10 + -10 = 0
0 + e = 9.486832981 + -10
e = 9.486832981 + -10

Combine like terms: 9.486832981 + -10 = -0.513167019
e = -0.513167019

Simplifying
e = -0.513167019


Subproblem 2
e + 10 = -9.486832981

Simplifying
e + 10 = -9.486832981

Reorder the terms:
10 + e = -9.486832981

Solving
10 + e = -9.486832981

Solving for variable 'e'.

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

Add '-10' to each side of the equation.
10 + -10 + e = -9.486832981 + -10

Combine like terms: 10 + -10 = 0
0 + e = -9.486832981 + -10
e = -9.486832981 + -10

Combine like terms: -9.486832981 + -10 = -19.486832981
e = -19.486832981

Simplifying
e = -19.486832981


Solution
The solution to the problem is based on the solutions
from the subproblems.
e = {-0.513167019, -19.486832981}

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