x2-12x+35=0

To solve the quadratic equation \(x^2 - 12x + 35 = 0\), we can use the factoring method. We look for two numbers that multiply to \(35\) (the constant term) and add up to \(-12\) (the coefficient of \(x\)).

The two numbers that satisfy these conditions are \(-5\) and \(-7\) because:

• \(-5 \times -7 = 35\)
• \(-5 + -7 = -12\)

Now we can factor the quadratic equation:

\[ (x - 5)(x - 7) = 0 \]

Next, we set each factor to zero:

1. \(x - 5 = 0\) ⟹ \(x = 5\)
2. \(x - 7 = 0\) ⟹ \(x = 7\)

Therefore, the solutions to the equation \(x^2 - 12x + 35 = 0\) are:

\[ x = 5 \quad \text{and} \quad x = 7 \]