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