Final answer:
To solve the equation w²-6w+9=0, we can use the quadratic formula. The solutions to the equation are w = 3.
Step-by-step explanation:
To solve the equation w²-6w+9=0, we can use the quadratic formula. For an equation of the form ax²+bx+c=0, the quadratic formula is:
w = (-b ± √(b²-4ac))/(2a).
In this case, a=1, b=-6, and c=9. Substituting these values into the quadratic formula, we get:
w = (-(-6) ± √((-6)²-4(1)(9)))/(2(1)).
Simplifying further, we have:
w = (6 ± √(36-36))/(2).
Now, since √(36-36) = √0 = 0, we have:
w = (6 ± 0)/(2).
Thus, the solutions to the equation are:
w = 6/2 = 3.