X²-7x+6=0

To solve the quadratic equation \( x^2 - 7x + 6 = 0 \), you can use the factoring method. We need to find two numbers that multiply to \( 6 \) (the constant term) and add up to \( -7 \) (the coefficient of \( x \)).

The numbers that satisfy both conditions are \( -1 \) and \( -6 \). Therefore, we can factor the equation as follows:

\[ (x - 1)(x - 6) = 0 \]

Now, we can set each factor equal to zero:

1. \( x - 1 = 0 \) → \( x = 1 \)
2. \( x - 6 = 0 \) → \( x = 6 \)

The solutions to the equation \( x^2 - 7x + 6 = 0 \) are:

\[ x = 1 \quad \text{and} \quad x = 6 \]