Solve the equation using the quadratic formula.
Square[x]+13x+7=0

The quadratic equation given is:

\[
x^2 + 13x + 7 = 0
\]

To solve this using the quadratic formula, we use the formula:

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

In this equation, \( a = 1 \), \( b = 13 \), and \( c = 7 \). Plugging in these values:

\[
x = \frac{-13 \pm \sqrt{13^2 - 4(1)(7)}}{2(1)}
\]

First, calculate the discriminant:

\[
\text{Discriminant} = 13^2 - 4(1)(7) = 169 - 28 = 141
\]

So, the equation becomes:

\[
x = \frac{-13 \pm \sqrt{141}}{2}
\]

This gives us two solutions:

\[
x_1 = \frac{-13 + \sqrt{141}}{2}
\]
\[
x_2 = \frac{-13 - \sqrt{141}}{2}
\]

These are the solutions to the equation.

Would you like more details, or do you have any questions?

Here are five related questions to explore further:
1. What does the discriminant tell us about the nature of the roots?
2. How can you approximate the solutions to the nearest decimal?
3. How does the quadratic formula change if \(b = 0\)?
4. What are the possible real-life applications of solving quadratic equations?
5. How would the graph of this quadratic equation look?

**Tip:** The discriminant can help you quickly determine whether the roots are real or complex.

Learn how to solve the quadratic equation x^2 + 13x + 7 with a step-by-step solution using the quadratic formula. This problem covers key algebraic concepts, including the quadratic formula and discriminant calculation. Suitable for students in Grades 10-12.

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