12.26x^2+31.25x+8.03=0

Solution for 12.26x^2+31.25x+8.03=0 equation:

Simplifying
12.26x2 + 31.25x + 8.03 = 0

Reorder the terms:
8.03 + 31.25x + 12.26x2 = 0

Solving
8.03 + 31.25x + 12.26x2 = 0

Solving for variable 'x'.

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

Divide each side by '12.26'.
0.6549755302 + 2.548939641x + x2 = 0

Move the constant term to the right:

Add '-0.6549755302' to each side of the equation.
0.6549755302 + 2.548939641x + -0.6549755302 + x2 = 0 + -0.6549755302

Reorder the terms:
0.6549755302 + -0.6549755302 + 2.548939641x + x2 = 0 + -0.6549755302

Combine like terms: 0.6549755302 + -0.6549755302 = 0.0000000000
0.0000000000 + 2.548939641x + x2 = 0 + -0.6549755302
2.548939641x + x2 = 0 + -0.6549755302

Combine like terms: 0 + -0.6549755302 = -0.6549755302
2.548939641x + x2 = -0.6549755302

The x term is 2.548939641x.  Take half its coefficient (1.274469821).
Square it (1.624273325) and add it to both sides.

Add '1.624273325' to each side of the equation.
2.548939641x + 1.624273325 + x2 = -0.6549755302 + 1.624273325

Reorder the terms:
1.624273325 + 2.548939641x + x2 = -0.6549755302 + 1.624273325

Combine like terms: -0.6549755302 + 1.624273325 = 0.9692977948
1.624273325 + 2.548939641x + x2 = 0.9692977948

Factor a perfect square on the left side:
(x + 1.274469821)(x + 1.274469821) = 0.9692977948

Calculate the square root of the right side: 0.984529225

Break this problem into two subproblems by setting 
(x + 1.274469821) equal to 0.984529225 and -0.984529225.

Subproblem 1
x + 1.274469821 = 0.984529225

Simplifying
x + 1.274469821 = 0.984529225

Reorder the terms:
1.274469821 + x = 0.984529225

Solving
1.274469821 + x = 0.984529225

Solving for variable 'x'.

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

Add '-1.274469821' to each side of the equation.
1.274469821 + -1.274469821 + x = 0.984529225 + -1.274469821

Combine like terms: 1.274469821 + -1.274469821 = 0.000000000
0.000000000 + x = 0.984529225 + -1.274469821
x = 0.984529225 + -1.274469821

Combine like terms: 0.984529225 + -1.274469821 = -0.289940596
x = -0.289940596

Simplifying
x = -0.289940596

Subproblem 2
x + 1.274469821 = -0.984529225

Simplifying
x + 1.274469821 = -0.984529225

Reorder the terms:
1.274469821 + x = -0.984529225

Solving
1.274469821 + x = -0.984529225

Solving for variable 'x'.

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

Add '-1.274469821' to each side of the equation.
1.274469821 + -1.274469821 + x = -0.984529225 + -1.274469821

Combine like terms: 1.274469821 + -1.274469821 = 0.000000000
0.000000000 + x = -0.984529225 + -1.274469821
x = -0.984529225 + -1.274469821

Combine like terms: -0.984529225 + -1.274469821 = -2.258999046
x = -2.258999046

Simplifying
x = -2.258999046

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.289940596, -2.258999046}