Final answer:
To solve x^2-6x+12=0 using the quadratic formula, we identify a=1, b=-6, and c=12, and substitute these into the formula. However, the equation has no real solutions because the discriminant is negative, indicating two complex solutions.
Step-by-step explanation:
The student asked how to solve the quadratic equation x^2-6x+12=0 using the quadratic formula. The quadratic formula for an equation of the form ax^2+bx+c=0 is given by x = (-b±√(b^2-4ac))/(2a). We can identify a=1, b=-6, and c=12 from the student's equation.
Plugging these values into the quadratic formula:
x = (6±√((-6)^2-4(1)(12)))/(2(1))
x = (6±√(36-48))/(2)
x = (6±√(-12))/(2)
Since the discriminant (the value under the square root) is negative, this equation has no real solutions; instead, it has two complex solutions.