Question

Which value of \(x\) is a solution to this equation?
\(8x^2-2x-3=0\)
(1 point)
8
-0.5
-3
4.5

Answer 1

To determine which value of \(x\) is a solution to the equation \(8x^2 - 2x - 3 = 0\), we can substitute each option into the equation and see if it results in a true statement.

1. **Testing \(x = 8\)**:
\[
8(8)^2 - 2(8) - 3 = 8 \cdot 64 - 16 - 3 = 512 - 16 - 3 = 493 \quad (\text{not } 0)
\]

2. **Testing \(x = -0.5\)**:
\[
8(-0.5)^2 - 2(-0.5) - 3 = 8 \cdot 0.25 + 1 - 3 = 2 + 1 - 3 = 0 \quad (\text{solution!})
\]

3. **Testing \(x = -3\)**:
\[
8(-3)^2 - 2(-3) - 3 = 8 \cdot 9 + 6 - 3 = 72 + 6 - 3 = 75 \quad (\text{not } 0)
\]

4. **Testing \(x = 4.5\)**:
\[
8(4.5)^2 - 2(4.5) - 3 = 8 \cdot 20.25 - 9 - 3 = 162 - 9 - 3 = 150 \quad (\text{not } 0)
\]

The only \(x\) that satisfies the equation \(8x^2 - 2x - 3 = 0\) is:

\[
\boxed{-0.5}
\]