8x^2=-2x-6

Solution for 8x^2=-2x-6 equation:

Simplifying
8x2 = -2x + -6

Reorder the terms:
8x2 = -6 + -2x

Solving
8x2 = -6 + -2x

Solving for variable 'x'.

Reorder the terms:
6 + 2x + 8x2 = -6 + -2x + 6 + 2x

Reorder the terms:
6 + 2x + 8x2 = -6 + 6 + -2x + 2x

Combine like terms: -6 + 6 = 0
6 + 2x + 8x2 = 0 + -2x + 2x
6 + 2x + 8x2 = -2x + 2x

Combine like terms: -2x + 2x = 0
6 + 2x + 8x2 = 0

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

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + x + 4x2)' equal to zero and attempt to solve:

Simplifying
3 + x + 4x2 = 0

Solving
3 + x + 4x2 = 0

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

Divide each side by '4'.
0.75 + 0.25x + x2 = 0

Move the constant term to the right:

Add '-0.75' to each side of the equation.
0.75 + 0.25x + -0.75 + x2 = 0 + -0.75

Reorder the terms:
0.75 + -0.75 + 0.25x + x2 = 0 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + 0.25x + x2 = 0 + -0.75
0.25x + x2 = 0 + -0.75

Combine like terms: 0 + -0.75 = -0.75
0.25x + x2 = -0.75

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.
0.25x + 0.25 + x2 = -0.75 + 0.25

Reorder the terms:
0.25 + 0.25x + x2 = -0.75 + 0.25

Combine like terms: -0.75 + 0.25 = -0.5
0.25 + 0.25x + x2 = -0.5

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

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.