Question

Which value of x
is a solution to this equation?

8x2−2x−3=0


(1 point)
Responses

8
8

-0.5
-0.5

-3
-3

4.5

Answer 1

To solve the equation \(8x^2 - 2x - 3 = 0\), we can use the quadratic formula:

\[
x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}
\]

In this case, \(a = 8\), \(b = -2\), and \(c = -3\).

First, we calculate the discriminant:

\[
b^2 - 4ac = (-2)^2 - 4 \cdot 8 \cdot (-3) = 4 + 96 = 100
\]

Next, we can plug the values into the formula:

\[
x = \frac{{-(-2) \pm \sqrt{100}}}{{2 \cdot 8}} = \frac{{2 \pm 10}}{{16}}
\]

This leads to two possible solutions:

1. \(x = \frac{{12}}{{16}} = \frac{3}{4} = 0.75\)
2. \(x = \frac{{-8}}{{16}} = -\frac{1}{2} = -0.5\)

Now, from the responses provided, the solution is:

\(-0.5\)

So the correct answer is \(-0.5\).