Question

x² - 8x - 65 = 0

Explanation:

Step1: Factor the quadratic equation

We need to find two numbers that multiply to \(-65\) and add up to \(-8\). The numbers are \(-13\) and \(5\) since \(-13\times5 = -65\) and \(-13 + 5=-8\). So we can factor the equation as:
\(x^{2}-8x - 65=(x - 13)(x + 5)=0\)

Step2: Solve for \(x\)

Set each factor equal to zero:

• For \(x - 13 = 0\), we get \(x = 13\).
• For \(x + 5 = 0\), we get \(x=-5\).

Answer:

The solutions are \(x = 13\) and \(x=-5\)