3e-19=-2e(e+2)

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Solution for 3e-19=-2e(e+2) equation: 


Simplifying
3e + -19 = -2e(e + 2)

Reorder the terms:
-19 + 3e = -2e(e + 2)

Reorder the terms:
-19 + 3e = -2e(2 + e)
-19 + 3e = (2 * -2e + e * -2e)
-19 + 3e = (-4e + -2e2)

Solving
-19 + 3e = -4e + -2e2

Solving for variable 'e'.

Combine like terms: 3e + 4e = 7e
-19 + 7e + 2e2 = -4e + -2e2 + 4e + 2e2

Reorder the terms:
-19 + 7e + 2e2 = -4e + 4e + -2e2 + 2e2

Combine like terms: -4e + 4e = 0
-19 + 7e + 2e2 = 0 + -2e2 + 2e2
-19 + 7e + 2e2 = -2e2 + 2e2

Combine like terms: -2e2 + 2e2 = 0
-19 + 7e + 2e2 = 0

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

Divide each side by '2'.
-9.5 + 3.5e + e2 = 0

Move the constant term to the right:

Add '9.5' to each side of the equation.
-9.5 + 3.5e + 9.5 + e2 = 0 + 9.5

Reorder the terms:
-9.5 + 9.5 + 3.5e + e2 = 0 + 9.5

Combine like terms: -9.5 + 9.5 = 0.0
0.0 + 3.5e + e2 = 0 + 9.5
3.5e + e2 = 0 + 9.5

Combine like terms: 0 + 9.5 = 9.5
3.5e + e2 = 9.5

The e term is 3.5e.  Take half its coefficient (1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
3.5e + 3.0625 + e2 = 9.5 + 3.0625

Reorder the terms:
3.0625 + 3.5e + e2 = 9.5 + 3.0625

Combine like terms: 9.5 + 3.0625 = 12.5625
3.0625 + 3.5e + e2 = 12.5625

Factor a perfect square on the left side:
(e + 1.75)(e + 1.75) = 12.5625

Calculate the square root of the right side: 3.54436172

Break this problem into two subproblems by setting 
(e + 1.75) equal to 3.54436172 and -3.54436172.


Subproblem 1
e + 1.75 = 3.54436172

Simplifying
e + 1.75 = 3.54436172

Reorder the terms:
1.75 + e = 3.54436172

Solving
1.75 + e = 3.54436172

Solving for variable 'e'.

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

Add '-1.75' to each side of the equation.
1.75 + -1.75 + e = 3.54436172 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + e = 3.54436172 + -1.75
e = 3.54436172 + -1.75

Combine like terms: 3.54436172 + -1.75 = 1.79436172
e = 1.79436172

Simplifying
e = 1.79436172


Subproblem 2
e + 1.75 = -3.54436172

Simplifying
e + 1.75 = -3.54436172

Reorder the terms:
1.75 + e = -3.54436172

Solving
1.75 + e = -3.54436172

Solving for variable 'e'.

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

Add '-1.75' to each side of the equation.
1.75 + -1.75 + e = -3.54436172 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + e = -3.54436172 + -1.75
e = -3.54436172 + -1.75

Combine like terms: -3.54436172 + -1.75 = -5.29436172
e = -5.29436172

Simplifying
e = -5.29436172


Solution
The solution to the problem is based on the solutions
from the subproblems.
e = {1.79436172, -5.29436172}

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