To solve the quadratic equation \( x^2 + 23x + 3 = 0 \), we can use the quadratic formula:

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

Here, \( a = 1 \), \( b = 23 \), and \( c = 3 \). Plugging these values into the formula, we get:

\[ x = \frac{-23 \pm \sqrt{23^2 - 4 \cdot 1 \cdot 3}}{2 \cdot 1} \]

\[ x = \frac{-23 \pm \sqrt{529 - 12}}{2} \]

\[ x = \frac{-23 \pm \sqrt{517}}{2} \]

So, the solutions to the quadratic equation \( x^2 + 23x + 3 = 0 \) are:

\[ x = \frac{-23 + \sqrt{517}}{2} \]
\[ x = \frac{-23 - \sqrt{517}}{2} \]

Would you like more details or have any questions about this solution?

Here are 5 more questions you might consider asking:

1. How do you complete the square for a quadratic equation?
2. Can you explain the quadratic formula derivation?
3. How do you factorize quadratic equations?
4. What are the properties of the roots of a quadratic equation?
5. How do you solve quadratic equations using the graphing method?

**Tip:** When solving quadratic equations, always check if it can be factorized easily before applying the quadratic formula for a quicker solution.

Learn how to solve the quadratic equation x^2 + 23x + 3 with a detailed step-by-step solution. This problem covers key algebraic concepts, including the quadratic formula and finding roots of equations. Suitable for students in Grades 10-12.

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