6x^2+22x+48=0

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Solution for 6x^2+22x+48=0 equation: 


Simplifying
6x2 + 22x + 48 = 0

Reorder the terms:
48 + 22x + 6x2 = 0

Solving
48 + 22x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(24 + 11x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(24 + 11x + 3x2)' equal to zero and attempt to solve:

Simplifying
24 + 11x + 3x2 = 0

Solving
24 + 11x + 3x2 = 0

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

Divide each side by '3'.
8 + 3.666666667x + x2 = 0

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + 3.666666667x + -8 + x2 = 0 + -8

Reorder the terms:
8 + -8 + 3.666666667x + x2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 3.666666667x + x2 = 0 + -8
3.666666667x + x2 = 0 + -8

Combine like terms: 0 + -8 = -8
3.666666667x + x2 = -8

The x term is 3.666666667x.  Take half its coefficient (1.833333334).
Square it (3.361111114) and add it to both sides.

Add '3.361111114' to each side of the equation.
3.666666667x + 3.361111114 + x2 = -8 + 3.361111114

Reorder the terms:
3.361111114 + 3.666666667x + x2 = -8 + 3.361111114

Combine like terms: -8 + 3.361111114 = -4.638888886
3.361111114 + 3.666666667x + x2 = -4.638888886

Factor a perfect square on the left side:
(x + 1.833333334)(x + 1.833333334) = -4.638888886

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.

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