Solve `(x-6)^(2)=0`.

Explanation

In this case, `x=6` twice, so x=6 is said to have multilicity 2.
The Quadratic formula `x=(-b+-sqrt(b^(2)-4ac))/(2a)` can be used to obtain the exact solutions of any quadratic equation of the form `ax^(2)+bx+c=0`. This formula is the result of completing the square for the general quadratic.
the expression `b^(2)-4ac` under the radical in the quadratic formula is called the discriminant. if the discriminant is positive, there are two real roots. if the discriminant is zero, there is one root of multiplicity 2. if the discriminant is negative, there is a conjugate pair of imaginary roots.
Note also that the two solutions given in the quadratic formula are conjugates u+v and `u-v,` where `u=-(b)/(2b) and v=(sqrt(b^(2)-4ac))/(2a)`. this implies that the sum of the root of a quadratic equation is `2u=2(-(b)/(2a))=-(b)/(a)` while the product of the roots is `u^(2)-v=(b^(2))/(4a^(2))-(b^(2)-4ac)/(4a^(2))=(4ac)/(4a^(2))=(c)/(a)`.