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We are asked to solve the quadratic equation:

\[
8x^2 - 5x - 4 = 0
\]

This is a standard quadratic equation of the form \( ax^2 + bx + c = 0 \), where:
- \( a = 8 \)
- \( b = -5 \)
- \( c = -4 \)

We can solve this using the quadratic formula:

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

Let's calculate the discriminant (\( \Delta \)) first:

\[
\Delta = b^2 - 4ac = (-5)^2 - 4(8)(-4) = 25 + 128 = 153
\]

Now substitute this into the quadratic formula:

\[
x = \frac{-(-5) \pm \sqrt{153}}{2(8)} = \frac{5 \pm \sqrt{153}}{16}
\]

We now need to find the two roots by calculating \( \sqrt{153} \approx 12.37 \) to three significant figures. Thus:

\[
x_1 = \frac{5 + 12.37}{16} = \frac{17.37}{16} \approx 1.086
\]
\[
x_2 = \frac{5 - 12.37}{16} = \frac{-7.37}{16} \approx -0.461
\]

So the two solutions are:

\[
x_1 \approx 1.09 \quad \text{(to 3 significant figures)}
\]
\[
x_2 \approx -0.461 \quad \text{(to 3 significant figures)}
\]

Would you like further explanation or details?

Here are 5 related questions to explore:
1. How does the discriminant affect the nature of the solutions to a quadratic equation?
2. Can we solve a quadratic equation using factoring methods instead of the quadratic formula?
3. How would the graph of \( y = 8x^2 - 5x - 4 \) look?
4. What are the vertex and axis of symmetry for the quadratic equation?
5. Can quadratic equations always be solved using the quadratic formula?

**Tip:** Always calculate the discriminant first to check whether a quadratic equation has real, repeated, or complex solutions.

Solve the quadratic equation 8x^2 - 5x - 4 = 0. Give your answers to 3 significant figures.

Learn how to solve the quadratic equation 8x^2 - 5x - 4 using the quadratic formula. This detailed explanation covers calculating the discriminant and finding the roots to three significant figures. Ideal for students in Grades 8-10.

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