24x^2+6x+8=0

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Solution for 24x^2+6x+8=0 equation: 


Simplifying
24x2 + 6x + 8 = 0

Reorder the terms:
8 + 6x + 24x2 = 0

Solving
8 + 6x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + 3x + 12x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(4 + 3x + 12x2)' equal to zero and attempt to solve:

Simplifying
4 + 3x + 12x2 = 0

Solving
4 + 3x + 12x2 = 0

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

Divide each side by '12'.
0.3333333333 + 0.25x + x2 = 0

Move the constant term to the right:

Add '-0.3333333333' to each side of the equation.
0.3333333333 + 0.25x + -0.3333333333 + x2 = 0 + -0.3333333333

Reorder the terms:
0.3333333333 + -0.3333333333 + 0.25x + x2 = 0 + -0.3333333333

Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000
0.0000000000 + 0.25x + x2 = 0 + -0.3333333333
0.25x + x2 = 0 + -0.3333333333

Combine like terms: 0 + -0.3333333333 = -0.3333333333
0.25x + x2 = -0.3333333333

The x term is 0.25x.  Take half its coefficient (0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
0.25x + 0.015625 + x2 = -0.3333333333 + 0.015625

Reorder the terms:
0.015625 + 0.25x + x2 = -0.3333333333 + 0.015625

Combine like terms: -0.3333333333 + 0.015625 = -0.3177083333
0.015625 + 0.25x + x2 = -0.3177083333

Factor a perfect square on the left side:
(x + 0.125)(x + 0.125) = -0.3177083333

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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