x²-6x+5=0

To solve the quadratic equation \(x^2 - 6x + 5 = 0\), you can either factor it or use the quadratic formula. In this case, it can be factored easily.

1. Factoring the equation: We want to express \(x^2 - 6x + 5\) in the form \((x - a)(x - b) = 0\). We need two numbers that multiply to \(5\) (the constant term) and add up to \(-6\) (the coefficient of \(x\)). The numbers \(-5\) and \(-1\) satisfy these conditions: \[ (x - 5)(x - 1) = 0 \]

2. Setting each factor to zero: \[ x - 5 = 0 \quad \text{or} \quad x - 1 = 0 \] This gives us the solutions: \[ x = 5 \quad \text{or} \quad x = 1 \]

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