6x^2+3x+24=3

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Solution for 6x^2+3x+24=3 equation: 


Simplifying
6x2 + 3x + 24 = 3

Reorder the terms:
24 + 3x + 6x2 = 3

Solving
24 + 3x + 6x2 = 3

Solving for variable 'x'.

Reorder the terms:
24 + -3 + 3x + 6x2 = 3 + -3

Combine like terms: 24 + -3 = 21
21 + 3x + 6x2 = 3 + -3

Combine like terms: 3 + -3 = 0
21 + 3x + 6x2 = 0

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

Ignore the factor 3.

Subproblem 1
Set the factor '(7 + x + 2x2)' equal to zero and attempt to solve:

Simplifying
7 + x + 2x2 = 0

Solving
7 + x + 2x2 = 0

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

Divide each side by '2'.
3.5 + 0.5x + x2 = 0

Move the constant term to the right:

Add '-3.5' to each side of the equation.
3.5 + 0.5x + -3.5 + x2 = 0 + -3.5

Reorder the terms:
3.5 + -3.5 + 0.5x + x2 = 0 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + 0.5x + x2 = 0 + -3.5
0.5x + x2 = 0 + -3.5

Combine like terms: 0 + -3.5 = -3.5
0.5x + x2 = -3.5

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.5x + 0.25 + x2 = -3.5 + 0.25

Reorder the terms:
0.25 + 0.5x + x2 = -3.5 + 0.25

Combine like terms: -3.5 + 0.25 = -3.25
0.25 + 0.5x + x2 = -3.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -3.25

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.

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