0=2x^2+8x+3

Solution for 0=2x^2+8x+3 equation:

Simplifying
0 = 2x2 + 8x + 3

Reorder the terms:
0 = 3 + 8x + 2x2

Solving
0 = 3 + 8x + 2x2

Solving for variable 'x'.

Combine like terms: 0 + -3 = -3
-3 + -8x + -2x2 = 3 + 8x + 2x2 + -3 + -8x + -2x2

Reorder the terms:
-3 + -8x + -2x2 = 3 + -3 + 8x + -8x + 2x2 + -2x2

Combine like terms: 3 + -3 = 0
-3 + -8x + -2x2 = 0 + 8x + -8x + 2x2 + -2x2
-3 + -8x + -2x2 = 8x + -8x + 2x2 + -2x2

Combine like terms: 8x + -8x = 0
-3 + -8x + -2x2 = 0 + 2x2 + -2x2
-3 + -8x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-3 + -8x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(3 + 8x + 2x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(3 + 8x + 2x2)' equal to zero and attempt to solve:

Simplifying
3 + 8x + 2x2 = 0

Solving
3 + 8x + 2x2 = 0

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

Divide each side by '2'.
1.5 + 4x + x2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + 4x + -1.5 + x2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + 4x + x2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + 4x + x2 = 0 + -1.5
4x + x2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
4x + x2 = -1.5

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = -1.5 + 4

Reorder the terms:
4 + 4x + x2 = -1.5 + 4

Combine like terms: -1.5 + 4 = 2.5
4 + 4x + x2 = 2.5

Factor a perfect square on the left side:
(x + 2)(x + 2) = 2.5

Calculate the square root of the right side: 1.58113883

Break this problem into two subproblems by setting 
(x + 2) equal to 1.58113883 and -1.58113883.

Subproblem 1
x + 2 = 1.58113883

Simplifying
x + 2 = 1.58113883

Reorder the terms:
2 + x = 1.58113883

Solving
2 + x = 1.58113883

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = 1.58113883 + -2

Combine like terms: 2 + -2 = 0
0 + x = 1.58113883 + -2
x = 1.58113883 + -2

Combine like terms: 1.58113883 + -2 = -0.41886117
x = -0.41886117

Simplifying
x = -0.41886117

Subproblem 2
x + 2 = -1.58113883

Simplifying
x + 2 = -1.58113883

Reorder the terms:
2 + x = -1.58113883

Solving
2 + x = -1.58113883

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = -1.58113883 + -2

Combine like terms: 2 + -2 = 0
0 + x = -1.58113883 + -2
x = -1.58113883 + -2

Combine like terms: -1.58113883 + -2 = -3.58113883
x = -3.58113883

Simplifying
x = -3.58113883

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.41886117, -3.58113883}
Solution
x = {-0.41886117, -3.58113883}