To solve the quadratic equation $5x^2 + 4x - 788 = 0$, we can apply the quadratic formula:

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

Where:

• $a = 5$
• $b = 4$
• $c = -788$

Now, let's substitute the values into the quadratic formula and solve for $x$.

$x = \frac{-4 \pm \sqrt{4^2 - 4(5)(-788)}}{2(5)}$

$x = \frac{-4 \pm \sqrt{16 + 15760}}{10}$

$x = \frac{-4 \pm \sqrt{15776}}{10}$

The square root of 15776 is 125.62 (approximately), so:

$x = \frac{-4 \pm 125.62}{10}$

Now we calculate the two possible solutions:

1. $x_1 = \frac{-4 + 125.62}{10} = \frac{121.62}{10} = 12.162$
2. $x_2 = \frac{-4 - 125.62}{10} = \frac{-129.62}{10} = -12.962$

Thus, the two solutions are approximately: $x_1 \approx 12.162 \quad \text{and} \quad x_2 \approx -12.962$

Would you like more details or have any questions?

Related questions:

1. How is the quadratic formula derived?
2. What are the alternative methods for solving quadratic equations?
3. How does the discriminant $b^2 - 4ac$ determine the nature of the roots?
4. Can all quadratic equations be solved using the quadratic formula?
5. What are some real-life applications of quadratic equations?

Tip: Always check the discriminant before solving with the quadratic formula to determine if the roots are real or complex.