x²-6x+5=0

To solve the quadratic equation \(x^2 - 6x + 5 = 0\), you can use the factoring method.

1. First, look for two numbers that multiply to \(5\) (the constant term) and add up to \(-6\) (the coefficient of the x term).

   • The numbers \(-1\) and \(-5\) fit this requirement since: \(-1 \cdot -5 = 5\) and \(-1 + -5 = -6\).

2. Therefore, we can factor the equation as: \[ (x - 1)(x - 5) = 0 \]

3. Now, set each factor equal to zero: \[ x - 1 = 0 \quad \text{or} \quad x - 5 = 0 \]

4. Solving these gives: \[ x = 1 \quad \text{or} \quad x = 5 \]

So the solutions to the equation \(x^2 - 6x + 5 = 0\) are \(x = 1\) and \(x = 5\).