What are the possible values of x in 8x2 + 4x = -1?

x only can have complex values, not real values.

x = -1/4 - 1/4i and x = -1/4 + 1/4 i

Explanation:

Finding the possible values of x in the expression given is solving the quadratic equation.

8x² + 4x = - 1

Rearrange the terms:

8 (x² + x/2) = - 1 ← common factor 8 in the left side

x² + x/2 = - 1/8 ← division property

x² + x/2 + 1/16 = - 1/8 + 1/16 ← addition property

(x + 1/4)² = -1/8 + 1/16 ← -factor the perfect square trinomial in the left side

(x + 1/4)² = - 1/16 ← add the fractions in the right side

x + 1/4 = (+/-) √ (-1/16) ← square roots on both sides

x + 1/4 = (+/-) (1/4)i ← complex solution

x = - 1/4 +/- 1/4i

x = - 1/4 - 1/4i and x = - 1/4 + 1/4 i ← answer