Question

1. ( x^2 - 14x + 13 = 0 )

Explanation:

Step1: Factor the quadratic equation

We need to find two numbers that multiply to \(13\) and add up to \(-14\). The numbers are \(-1\) and \(-13\) since \((-1)\times(-13) = 13\) and \((-1)+(-13)=-14\). So we can factor the equation as:
\(x^{2}-14x + 13=(x - 1)(x - 13)=0\)

Step2: Solve for \(x\)

Using the zero - product property, if \(ab = 0\), then either \(a = 0\) or \(b = 0\).
For \((x - 1)(x - 13)=0\), we have two cases:
Case 1: \(x-1=0\), then \(x = 1\).
Case 2: \(x - 13=0\), then \(x=13\).

Answer:

\(x = 1\) or \(x = 13\)