4.46x^2-11.26x+2.71=0

Solution for 4.46x^2-11.26x+2.71=0 equation:

Simplifying
4.46x2 + -11.26x + 2.71 = 0

Reorder the terms:
2.71 + -11.26x + 4.46x2 = 0

Solving
2.71 + -11.26x + 4.46x2 = 0

Solving for variable 'x'.

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

Divide each side by '4.46'.
0.6076233184 + -2.524663677x + x2 = 0

Move the constant term to the right:

Add '-0.6076233184' to each side of the equation.
0.6076233184 + -2.524663677x + -0.6076233184 + x2 = 0 + -0.6076233184

Reorder the terms:
0.6076233184 + -0.6076233184 + -2.524663677x + x2 = 0 + -0.6076233184

Combine like terms: 0.6076233184 + -0.6076233184 = 0.0000000000
0.0000000000 + -2.524663677x + x2 = 0 + -0.6076233184
-2.524663677x + x2 = 0 + -0.6076233184

Combine like terms: 0 + -0.6076233184 = -0.6076233184
-2.524663677x + x2 = -0.6076233184

The x term is -2.524663677x.  Take half its coefficient (-1.262331839).
Square it (1.593481672) and add it to both sides.

Add '1.593481672' to each side of the equation.
-2.524663677x + 1.593481672 + x2 = -0.6076233184 + 1.593481672

Reorder the terms:
1.593481672 + -2.524663677x + x2 = -0.6076233184 + 1.593481672

Combine like terms: -0.6076233184 + 1.593481672 = 0.9858583536
1.593481672 + -2.524663677x + x2 = 0.9858583536

Factor a perfect square on the left side:
(x + -1.262331839)(x + -1.262331839) = 0.9858583536

Calculate the square root of the right side: 0.992904

Break this problem into two subproblems by setting 
(x + -1.262331839) equal to 0.992904 and -0.992904.

Subproblem 1
x + -1.262331839 = 0.992904

Simplifying
x + -1.262331839 = 0.992904

Reorder the terms:
-1.262331839 + x = 0.992904

Solving
-1.262331839 + x = 0.992904

Solving for variable 'x'.

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

Add '1.262331839' to each side of the equation.
-1.262331839 + 1.262331839 + x = 0.992904 + 1.262331839

Combine like terms: -1.262331839 + 1.262331839 = 0.000000000
0.000000000 + x = 0.992904 + 1.262331839
x = 0.992904 + 1.262331839

Combine like terms: 0.992904 + 1.262331839 = 2.255235839
x = 2.255235839

Simplifying
x = 2.255235839

Subproblem 2
x + -1.262331839 = -0.992904

Simplifying
x + -1.262331839 = -0.992904

Reorder the terms:
-1.262331839 + x = -0.992904

Solving
-1.262331839 + x = -0.992904

Solving for variable 'x'.

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

Add '1.262331839' to each side of the equation.
-1.262331839 + 1.262331839 + x = -0.992904 + 1.262331839

Combine like terms: -1.262331839 + 1.262331839 = 0.000000000
0.000000000 + x = -0.992904 + 1.262331839
x = -0.992904 + 1.262331839

Combine like terms: -0.992904 + 1.262331839 = 0.269427839
x = 0.269427839

Simplifying
x = 0.269427839

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.255235839, 0.269427839}