x^2+3.1x+1.5=0

Solution for x^2+3.1x+1.5=0 equation:

Simplifying
x2 + 3.1x + 1.5 = 0

Reorder the terms:
1.5 + 3.1x + x2 = 0

Solving
1.5 + 3.1x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + 3.1x + -1.5 + x2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + 3.1x + x2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + 3.1x + x2 = 0 + -1.5
3.1x + x2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
3.1x + x2 = -1.5

The x term is 3.1x.  Take half its coefficient (1.55).
Square it (2.4025) and add it to both sides.

Add '2.4025' to each side of the equation.
3.1x + 2.4025 + x2 = -1.5 + 2.4025

Reorder the terms:
2.4025 + 3.1x + x2 = -1.5 + 2.4025

Combine like terms: -1.5 + 2.4025 = 0.9025
2.4025 + 3.1x + x2 = 0.9025

Factor a perfect square on the left side:
(x + 1.55)(x + 1.55) = 0.9025

Calculate the square root of the right side: 0.95

Break this problem into two subproblems by setting 
(x + 1.55) equal to 0.95 and -0.95.

Subproblem 1
x + 1.55 = 0.95

Simplifying
x + 1.55 = 0.95

Reorder the terms:
1.55 + x = 0.95

Solving
1.55 + x = 0.95

Solving for variable 'x'.

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

Add '-1.55' to each side of the equation.
1.55 + -1.55 + x = 0.95 + -1.55

Combine like terms: 1.55 + -1.55 = 0.00
0.00 + x = 0.95 + -1.55
x = 0.95 + -1.55

Combine like terms: 0.95 + -1.55 = -0.6
x = -0.6

Simplifying
x = -0.6

Subproblem 2
x + 1.55 = -0.95

Simplifying
x + 1.55 = -0.95

Reorder the terms:
1.55 + x = -0.95

Solving
1.55 + x = -0.95

Solving for variable 'x'.

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

Add '-1.55' to each side of the equation.
1.55 + -1.55 + x = -0.95 + -1.55

Combine like terms: 1.55 + -1.55 = 0.00
0.00 + x = -0.95 + -1.55
x = -0.95 + -1.55

Combine like terms: -0.95 + -1.55 = -2.5
x = -2.5

Simplifying
x = -2.5

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.6, -2.5}