The equation in the image is:

$x^2 + 5x - 4 = 0$

To solve this quadratic equation, we can use the quadratic formula:

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

For the given equation $x^2 + 5x - 4 = 0$, the coefficients are:

• $a = 1$ (coefficient of $x^2$)
• $b = 5$ (coefficient of $x$)
• $c = -4$ (constant term)

Substituting these values into the quadratic formula:

$x = \frac{-5 \pm \sqrt{5^2 - 4(1)(-4)}}{2(1)}$

Simplifying further:

$x = \frac{-5 \pm \sqrt{25 + 16}}{2}$ $x = \frac{-5 \pm \sqrt{41}}{2}$

So, the two solutions are:

$x_1 = \frac{-5 + \sqrt{41}}{2} \quad \text{and} \quad x_2 = \frac{-5 - \sqrt{41}}{2}$

These are the exact solutions for the quadratic equation.

Would you like more details on the process or have any questions?

Here are 5 related questions that expand on this topic:

1. What is the quadratic formula used for, and why does it work?
2. How can you determine the nature of the roots using the discriminant?
3. What are the possible types of roots a quadratic equation can have?
4. How can quadratic equations be solved by factoring?
5. What are some real-life applications of solving quadratic equations?

Tip: When solving quadratic equations, always check if the equation can be factored easily before applying the quadratic formula; factoring can be quicker and simpler in many cases.