To solve the quadratic equation $x^2 + 6x - 7 = 0$, we can apply the quadratic formula:

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

For the given equation $x^2 + 6x - 7 = 0$, the coefficients are:

• $a = 1$
• $b = 6$
• $c = -7$

Step 1: Calculate the discriminant

$\Delta = b^2 - 4ac = 6^2 - 4(1)(-7) = 36 + 28 = 64$

Step 2: Apply the quadratic formula

$x = \frac{-6 \pm \sqrt{64}}{2(1)} = \frac{-6 \pm 8}{2}$

Step 3: Find the two solutions

$x_1 = \frac{-6 + 8}{2} = \frac{2}{2} = 1$ $x_2 = \frac{-6 - 8}{2} = \frac{-14}{2} = -7$

Final Solutions:

$x_1 = 1 \quad \text{and} \quad x_2 = -7$

Would you like more details or have any questions?

Here are some related questions to consider:

1. How does the discriminant affect the number of real solutions?
2. Can every quadratic equation be solved using the quadratic formula?
3. What are other methods for solving quadratic equations?
4. What does the graph of $x^2 + 6x - 7 = 0$ look like?
5. How can completing the square be used to solve this equation?

Tip: The discriminant, $\Delta$, tells you whether the solutions are real or complex. If $\Delta > 0$, there are two real solutions!