0=0.5x^2+3.5x+5

Solution for 0=0.5x^2+3.5x+5 equation:

Simplifying
0 = 0.5x2 + 3.5x + 5

Reorder the terms:
0 = 5 + 3.5x + 0.5x2

Solving
0 = 5 + 3.5x + 0.5x2

Solving for variable 'x'.

Combine like terms: 0 + -5 = -5
-5 + -3.5x + -0.5x2 = 5 + 3.5x + 0.5x2 + -5 + -3.5x + -0.5x2

Reorder the terms:
-5 + -3.5x + -0.5x2 = 5 + -5 + 3.5x + -3.5x + 0.5x2 + -0.5x2

Combine like terms: 5 + -5 = 0
-5 + -3.5x + -0.5x2 = 0 + 3.5x + -3.5x + 0.5x2 + -0.5x2
-5 + -3.5x + -0.5x2 = 3.5x + -3.5x + 0.5x2 + -0.5x2

Combine like terms: 3.5x + -3.5x = 0.0
-5 + -3.5x + -0.5x2 = 0.0 + 0.5x2 + -0.5x2
-5 + -3.5x + -0.5x2 = 0.5x2 + -0.5x2

Combine like terms: 0.5x2 + -0.5x2 = 0.0
-5 + -3.5x + -0.5x2 = 0.0

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

Divide each side by '-0.5'.
10 + 7x + x2 = 0

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + 7x + -10 + x2 = 0 + -10

Reorder the terms:
10 + -10 + 7x + x2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + 7x + x2 = 0 + -10
7x + x2 = 0 + -10

Combine like terms: 0 + -10 = -10
7x + x2 = -10

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 = -10 + 12.25

Reorder the terms:
12.25 + 7x + x2 = -10 + 12.25

Combine like terms: -10 + 12.25 = 2.25
12.25 + 7x + x2 = 2.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 2.25

Calculate the square root of the right side: 1.5

Break this problem into two subproblems by setting 
(x + 3.5) equal to 1.5 and -1.5.

Subproblem 1
x + 3.5 = 1.5

Simplifying
x + 3.5 = 1.5

Reorder the terms:
3.5 + x = 1.5

Solving
3.5 + x = 1.5

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 = 1.5 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 1.5 + -3.5
x = 1.5 + -3.5

Combine like terms: 1.5 + -3.5 = -2
x = -2

Simplifying
x = -2

Subproblem 2
x + 3.5 = -1.5

Simplifying
x + 3.5 = -1.5

Reorder the terms:
3.5 + x = -1.5

Solving
3.5 + x = -1.5

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 = -1.5 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -1.5 + -3.5
x = -1.5 + -3.5

Combine like terms: -1.5 + -3.5 = -5
x = -5

Simplifying
x = -5

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-2, -5}