0.5x^2+3.5x+3=0

Solution for 0.5x^2+3.5x+3=0 equation:

Simplifying
0.5x2 + 3.5x + 3 = 0

Reorder the terms:
3 + 3.5x + 0.5x2 = 0

Solving
3 + 3.5x + 0.5x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.5'.
6 + 7x + x2 = 0

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + 7x + -6 + x2 = 0 + -6

Reorder the terms:
6 + -6 + 7x + x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 7x + x2 = 0 + -6
7x + x2 = 0 + -6

Combine like terms: 0 + -6 = -6
7x + x2 = -6

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = -6 + 12.25

Reorder the terms:
12.25 + 7x + x2 = -6 + 12.25

Combine like terms: -6 + 12.25 = 6.25
12.25 + 7x + x2 = 6.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 6.25

Calculate the square root of the right side: 2.5

Break this problem into two subproblems by setting 
(x + 3.5) equal to 2.5 and -2.5.

Subproblem 1
x + 3.5 = 2.5

Simplifying
x + 3.5 = 2.5

Reorder the terms:
3.5 + x = 2.5

Solving
3.5 + x = 2.5

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = 2.5 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 2.5 + -3.5
x = 2.5 + -3.5

Combine like terms: 2.5 + -3.5 = -1
x = -1

Simplifying
x = -1

Subproblem 2
x + 3.5 = -2.5

Simplifying
x + 3.5 = -2.5

Reorder the terms:
3.5 + x = -2.5

Solving
3.5 + x = -2.5

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = -2.5 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -2.5 + -3.5
x = -2.5 + -3.5

Combine like terms: -2.5 + -3.5 = -6
x = -6

Simplifying
x = -6

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1, -6}