.5x^2+2x-6=0

Solution for .5x^2+2x-6=0 equation:

Simplifying
0.5x2 + 2x + -6 = 0

Reorder the terms:
-6 + 2x + 0.5x2 = 0

Solving
-6 + 2x + 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'.
-12 + 4x + x2 = 0

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + 4x + 12 + x2 = 0 + 12

Reorder the terms:
-12 + 12 + 4x + x2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + 4x + x2 = 0 + 12
4x + x2 = 0 + 12

Combine like terms: 0 + 12 = 12
4x + x2 = 12

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 = 12 + 4

Reorder the terms:
4 + 4x + x2 = 12 + 4

Combine like terms: 12 + 4 = 16
4 + 4x + x2 = 16

Factor a perfect square on the left side:
(x + 2)(x + 2) = 16

Calculate the square root of the right side: 4

Break this problem into two subproblems by setting 
(x + 2) equal to 4 and -4.

Subproblem 1
x + 2 = 4

Simplifying
x + 2 = 4

Reorder the terms:
2 + x = 4

Solving
2 + x = 4

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 = 4 + -2

Combine like terms: 2 + -2 = 0
0 + x = 4 + -2
x = 4 + -2

Combine like terms: 4 + -2 = 2
x = 2

Simplifying
x = 2

Subproblem 2
x + 2 = -4

Simplifying
x + 2 = -4

Reorder the terms:
2 + x = -4

Solving
2 + x = -4

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 = -4 + -2

Combine like terms: 2 + -2 = 0
0 + x = -4 + -2
x = -4 + -2

Combine like terms: -4 + -2 = -6
x = -6

Simplifying
x = -6

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2, -6}