4x^2=44x-122

Solution for 4x^2=44x-122 equation:

Simplifying
4x2 = 44x + -122

Reorder the terms:
4x2 = -122 + 44x

Solving
4x2 = -122 + 44x

Solving for variable 'x'.

Reorder the terms:
122 + -44x + 4x2 = -122 + 44x + 122 + -44x

Reorder the terms:
122 + -44x + 4x2 = -122 + 122 + 44x + -44x

Combine like terms: -122 + 122 = 0
122 + -44x + 4x2 = 0 + 44x + -44x
122 + -44x + 4x2 = 44x + -44x

Combine like terms: 44x + -44x = 0
122 + -44x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(61 + -22x + 2x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(61 + -22x + 2x2)' equal to zero and attempt to solve:

Simplifying
61 + -22x + 2x2 = 0

Solving
61 + -22x + 2x2 = 0

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

Divide each side by '2'.
30.5 + -11x + x2 = 0

Move the constant term to the right:

Add '-30.5' to each side of the equation.
30.5 + -11x + -30.5 + x2 = 0 + -30.5

Reorder the terms:
30.5 + -30.5 + -11x + x2 = 0 + -30.5

Combine like terms: 30.5 + -30.5 = 0.0
0.0 + -11x + x2 = 0 + -30.5
-11x + x2 = 0 + -30.5

Combine like terms: 0 + -30.5 = -30.5
-11x + x2 = -30.5

The x term is -11x.  Take half its coefficient (-5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
-11x + 30.25 + x2 = -30.5 + 30.25

Reorder the terms:
30.25 + -11x + x2 = -30.5 + 30.25

Combine like terms: -30.5 + 30.25 = -0.25
30.25 + -11x + x2 = -0.25

Factor a perfect square on the left side:
(x + -5.5)(x + -5.5) = -0.25

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.