6x^2+14x+24=0

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Solution for 6x^2+14x+24=0 equation: 


Simplifying
6x2 + 14x + 24 = 0

Reorder the terms:
24 + 14x + 6x2 = 0

Solving
24 + 14x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(12 + 7x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(12 + 7x + 3x2)' equal to zero and attempt to solve:

Simplifying
12 + 7x + 3x2 = 0

Solving
12 + 7x + 3x2 = 0

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

Divide each side by '3'.
4 + 2.333333333x + x2 = 0

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + 2.333333333x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + 2.333333333x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 2.333333333x + x2 = 0 + -4
2.333333333x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
2.333333333x + x2 = -4

The x term is 2.333333333x.  Take half its coefficient (1.166666667).
Square it (1.361111112) and add it to both sides.

Add '1.361111112' to each side of the equation.
2.333333333x + 1.361111112 + x2 = -4 + 1.361111112

Reorder the terms:
1.361111112 + 2.333333333x + x2 = -4 + 1.361111112

Combine like terms: -4 + 1.361111112 = -2.638888888
1.361111112 + 2.333333333x + x2 = -2.638888888

Factor a perfect square on the left side:
(x + 1.166666667)(x + 1.166666667) = -2.638888888

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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