.5x+x^2=0

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

Simplifying
0.5x + x2 = 0

Solving
0.5x + x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(0.5 + x) = 0

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(0.5 + x)' equal to zero and attempt to solve:

Simplifying
0.5 + x = 0

Solving
0.5 + x = 0

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 0 + -0.5
x = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
x = -0.5

Simplifying
x = -0.5
Solution
x = {0, -0.5}