12.905=((-6.72)X^2)+27.233X+4.1527

Solution for 12.905=((-6.72)X^2)+27.233X+4.1527 equation:

Simplifying
12.905 = ((-6.72) * X2) + 27.233X + 4.1527

Reorder the terms:
12.905 = 4.1527 + 27.233X + (-6.72X2)

Solving
12.905 = 4.1527 + 27.233X + (-6.72X2)

Solving for variable 'X'.

Combine like terms: 12.905 + -4.1527 = 8.7523
8.7523 + -27.233X + (6.72X2) = 4.1527 + 27.233X + (-6.72X2) + -4.1527 + -27.233X + (6.72X2)

Reorder the terms:
8.7523 + -27.233X + (6.72X2) = 4.1527 + -4.1527 + 27.233X + -27.233X + (-6.72X2) + (6.72X2)

Combine like terms: 4.1527 + -4.1527 = 0.0000
8.7523 + -27.233X + (6.72X2) = 0.0000 + 27.233X + -27.233X + (-6.72X2) + (6.72X2)
8.7523 + -27.233X + (6.72X2) = 27.233X + -27.233X + (-6.72X2) + (6.72X2)

Combine like terms: 27.233X + -27.233X = 0.000
8.7523 + -27.233X + (6.72X2) = 0.000 + (-6.72X2) + (6.72X2)
8.7523 + -27.233X + (6.72X2) = (-6.72X2) + (6.72X2)

Combine like terms: (-6.72X2) + (6.72X2) = 0.00
8.7523 + -27.233X + (6.72X2) = 0.00

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

Divide each side by '6.72'.
1.302425595 + -4.052529762X + X2 = 0

Move the constant term to the right:

Add '-1.302425595' to each side of the equation.
1.302425595 + -4.052529762X + -1.302425595 + X2 = 0 + -1.302425595

Reorder the terms:
1.302425595 + -1.302425595 + -4.052529762X + X2 = 0 + -1.302425595

Combine like terms: 1.302425595 + -1.302425595 = 0.000000000
0.000000000 + -4.052529762X + X2 = 0 + -1.302425595
-4.052529762X + X2 = 0 + -1.302425595

Combine like terms: 0 + -1.302425595 = -1.302425595
-4.052529762X + X2 = -1.302425595

The X term is -4.052529762X.  Take half its coefficient (-2.026264881).
Square it (4.105749368) and add it to both sides.

Add '4.105749368' to each side of the equation.
-4.052529762X + 4.105749368 + X2 = -1.302425595 + 4.105749368

Reorder the terms:
4.105749368 + -4.052529762X + X2 = -1.302425595 + 4.105749368

Combine like terms: -1.302425595 + 4.105749368 = 2.803323773
4.105749368 + -4.052529762X + X2 = 2.803323773

Factor a perfect square on the left side:
((X) + -2.026264881)((X) + -2.026264881) = 2.803323773

Calculate the square root of the right side: 1.674312926

Break this problem into two subproblems by setting 
((X) + -2.026264881) equal to 1.674312926 and -1.674312926.

Subproblem 1
(X) + -2.026264881 = 1.674312926

Simplifying
(X) + -2.026264881 = 1.674312926
X + -2.026264881 = 1.674312926

Reorder the terms:
-2.026264881 + X = 1.674312926

Solving
-2.026264881 + X = 1.674312926

Solving for variable 'X'.

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

Add '2.026264881' to each side of the equation.
-2.026264881 + 2.026264881 + X = 1.674312926 + 2.026264881

Combine like terms: -2.026264881 + 2.026264881 = 0.000000000
0.000000000 + X = 1.674312926 + 2.026264881
X = 1.674312926 + 2.026264881

Combine like terms: 1.674312926 + 2.026264881 = 3.700577807
X = 3.700577807

Simplifying
X = 3.700577807

Subproblem 2
(X) + -2.026264881 = -1.674312926

Simplifying
(X) + -2.026264881 = -1.674312926
X + -2.026264881 = -1.674312926

Reorder the terms:
-2.026264881 + X = -1.674312926

Solving
-2.026264881 + X = -1.674312926

Solving for variable 'X'.

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

Add '2.026264881' to each side of the equation.
-2.026264881 + 2.026264881 + X = -1.674312926 + 2.026264881

Combine like terms: -2.026264881 + 2.026264881 = 0.000000000
0.000000000 + X = -1.674312926 + 2.026264881
X = -1.674312926 + 2.026264881

Combine like terms: -1.674312926 + 2.026264881 = 0.351951955
X = 0.351951955

Simplifying
X = 0.351951955

Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {3.700577807, 0.351951955}