What value of x is in the solution set of 23x² – 8x – 6?

To find the value of x that satisfies the equation 23x² – 8x – 6 = 0, we can use the quadratic formula, which is given by:

x = (-b ± √(b² – 4ac)) / 2a

In this case, the coefficients are:

• a = 23
• b = -8
• c = -6

First, we need to calculate the discriminant (b² – 4ac):

Discriminant = (-8)² – 4(23)(-6)

Discriminant = 64 + 552

Discriminant = 616

Since the discriminant is positive, we will have two real solutions. Now, we can substitute back into the quadratic formula:

x = (8 ± √616) / (2 * 23)

Next, calculating the square root of 616 gives us approximately 24.8:

x = (8 ± 24.8) / 46

This leads us to two potential solutions:

1. x = (8 + 24.8) / 46 ≈ 0.71
2. x = (8 – 24.8) / 46 ≈ -0.37

Thus, the values of x in the solution set are approximately 0.71 and -0.37.