**Quadratic Equations: Solving x^2 + 10x + 24 = 0**

**Introduction**

In algebra, a quadratic equation is a polynomial equation of degree two, which means the highest power of the variable (usually x) is two. The general form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constants. In this article, we will focus on solving the quadratic equation x^2 + 10x + 24 = 0.

**Factoring Quadratics**

One way to solve quadratic equations is by factoring. Factoring involves expressing the quadratic equation as a product of two binomials. In this case, we can factor x^2 + 10x + 24 as:

x^2 + 10x + 24 = (x + 6)(x + 4) = 0

**Solutions**

Now that we have factored the quadratic equation, we can easily find the solutions by setting each factor equal to zero:

(x + 6)(x + 4) = 0

x + 6 = 0 or x + 4 = 0

x = -6 or x = -4

Therefore, the solutions to the quadratic equation x^2 + 10x + 24 = 0 are x = -6 and x = -4.

**Graphical Representation**

We can also graph the related function f(x) = x^2 + 10x + 24 to visualize the solutions.

! = x^2 + 10x + 24")

The graph shows that the function intersects the x-axis at x = -6 and x = -4, which confirms our algebraic solutions.

**Conclusion**

In this article, we have solved the quadratic equation x^2 + 10x + 24 = 0 using factoring. We have found that the solutions are x = -6 and x = -4, which are also evident from the graphical representation of the related function.