0.8x^2+5x+3.1=0

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Solution for 0.8x^2+5x+3.1=0 equation: 


Simplifying
0.8x2 + 5x + 3.1 = 0

Reorder the terms:
3.1 + 5x + 0.8x2 = 0

Solving
3.1 + 5x + 0.8x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.8'.
3.875 + 6.25x + x2 = 0

Move the constant term to the right:

Add '-3.875' to each side of the equation.
3.875 + 6.25x + -3.875 + x2 = 0 + -3.875

Reorder the terms:
3.875 + -3.875 + 6.25x + x2 = 0 + -3.875

Combine like terms: 3.875 + -3.875 = 0.000
0.000 + 6.25x + x2 = 0 + -3.875
6.25x + x2 = 0 + -3.875

Combine like terms: 0 + -3.875 = -3.875
6.25x + x2 = -3.875

The x term is 6.25x.  Take half its coefficient (3.125).
Square it (9.765625) and add it to both sides.

Add '9.765625' to each side of the equation.
6.25x + 9.765625 + x2 = -3.875 + 9.765625

Reorder the terms:
9.765625 + 6.25x + x2 = -3.875 + 9.765625

Combine like terms: -3.875 + 9.765625 = 5.890625
9.765625 + 6.25x + x2 = 5.890625

Factor a perfect square on the left side:
(x + 3.125)(x + 3.125) = 5.890625

Calculate the square root of the right side: 2.42706098

Break this problem into two subproblems by setting 
(x + 3.125) equal to 2.42706098 and -2.42706098.


Subproblem 1
x + 3.125 = 2.42706098

Simplifying
x + 3.125 = 2.42706098

Reorder the terms:
3.125 + x = 2.42706098

Solving
3.125 + x = 2.42706098

Solving for variable 'x'.

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

Add '-3.125' to each side of the equation.
3.125 + -3.125 + x = 2.42706098 + -3.125

Combine like terms: 3.125 + -3.125 = 0.000
0.000 + x = 2.42706098 + -3.125
x = 2.42706098 + -3.125

Combine like terms: 2.42706098 + -3.125 = -0.69793902
x = -0.69793902

Simplifying
x = -0.69793902


Subproblem 2
x + 3.125 = -2.42706098

Simplifying
x + 3.125 = -2.42706098

Reorder the terms:
3.125 + x = -2.42706098

Solving
3.125 + x = -2.42706098

Solving for variable 'x'.

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

Add '-3.125' to each side of the equation.
3.125 + -3.125 + x = -2.42706098 + -3.125

Combine like terms: 3.125 + -3.125 = 0.000
0.000 + x = -2.42706098 + -3.125
x = -2.42706098 + -3.125

Combine like terms: -2.42706098 + -3.125 = -5.55206098
x = -5.55206098

Simplifying
x = -5.55206098


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.69793902, -5.55206098}

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