15x^2+x+2=0

Solution for 15x^2+x+2=0 equation:

Simplifying
15x2 + x + 2 = 0

Reorder the terms:
2 + x + 15x2 = 0

Solving
2 + x + 15x2 = 0

Solving for variable 'x'.

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

Divide each side by '15'.
0.1333333333 + 0.06666666667x + x2 = 0

Move the constant term to the right:

Add '-0.1333333333' to each side of the equation.
0.1333333333 + 0.06666666667x + -0.1333333333 + x2 = 0 + -0.1333333333

Reorder the terms:
0.1333333333 + -0.1333333333 + 0.06666666667x + x2 = 0 + -0.1333333333

Combine like terms: 0.1333333333 + -0.1333333333 = 0.0000000000
0.0000000000 + 0.06666666667x + x2 = 0 + -0.1333333333
0.06666666667x + x2 = 0 + -0.1333333333

Combine like terms: 0 + -0.1333333333 = -0.1333333333
0.06666666667x + x2 = -0.1333333333

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.06666666667x + 0.25 + x2 = -0.1333333333 + 0.25

Reorder the terms:
0.25 + 0.06666666667x + x2 = -0.1333333333 + 0.25

Combine like terms: -0.1333333333 + 0.25 = 0.1166666667
0.25 + 0.06666666667x + x2 = 0.1166666667

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 0.1166666667

Calculate the square root of the right side: 0.341565026

Break this problem into two subproblems by setting 
(x + 0.5) equal to 0.341565026 and -0.341565026.

Subproblem 1
x + 0.5 = 0.341565026

Simplifying
x + 0.5 = 0.341565026

Reorder the terms:
0.5 + x = 0.341565026

Solving
0.5 + x = 0.341565026

Solving for variable 'x'.

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 = 0.341565026 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 0.341565026 + -0.5
x = 0.341565026 + -0.5

Combine like terms: 0.341565026 + -0.5 = -0.158434974
x = -0.158434974

Simplifying
x = -0.158434974

Subproblem 2
x + 0.5 = -0.341565026

Simplifying
x + 0.5 = -0.341565026

Reorder the terms:
0.5 + x = -0.341565026

Solving
0.5 + x = -0.341565026

Solving for variable 'x'.

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 = -0.341565026 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -0.341565026 + -0.5
x = -0.341565026 + -0.5

Combine like terms: -0.341565026 + -0.5 = -0.841565026
x = -0.841565026

Simplifying
x = -0.841565026

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.158434974, -0.841565026}