https://file.aiquickdraw.com/mathbot/file/1727410454416sq08k5w3.jpg

The equation in the image is:

\[
x^2 - 5x + 36 = 0
\]

To solve this by factoring, we need to express the quadratic in a factored form. However, the equation doesn't appear to be easily factorable with rational numbers, since no pair of numbers multiplies to 36 and adds up to -5.

Given this, it's likely that this quadratic doesn't factor neatly. So, we should instead use the quadratic formula:

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

For the equation \(x^2 - 5x + 36 = 0\), the coefficients are:
- \(a = 1\)
- \(b = -5\)
- \(c = 36\)

Let me calculate the solution for you.The equation \(x^2 - 5x + 36 = 0\) has complex roots, as the discriminant is negative. The solutions are:

\[
x = 2.5 + 5.45i \quad \text{and} \quad x = 2.5 - 5.45i
\]

Thus, this quadratic doesn't factor neatly into real numbers. If factoring over real numbers is required, this equation has no solution.

Would you like to explore more on this topic or have any further questions? Here are some related questions:

1. How do we handle complex numbers in quadratic equations?
2. Can we factor quadratics with complex roots?
3. What is the role of the discriminant in solving quadratics?
4. How do you graph quadratic functions with complex solutions?
5. Can every quadratic be solved using factoring?

**Tip:** Always check the discriminant \(\Delta = b^2 - 4ac\) to determine whether a quadratic can be factored with real or complex numbers.

Solve the quadratic equation by factoring: x^2 - 5x + 36 = 0.

Learn how to solve the quadratic equation x^2 - 5x + 36 using factoring and the quadratic formula. This algebraic concept involves determining the discriminant to check for real or complex solutions. Suitable for students in Grades 8-10.

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