Which of the following is a solution of x^2 -6x-22? -6-i square root 52 -6+i square root 13 3-i square root 13 -3+i square root 52

You could check these four answers by subbing them, one by one, into the original equation.  Or you could immediately apply the quadratic formula to  
x^2 -6x-22.  I'd rather be proactive and calculate the roots myself.

Using a=1, b= -6 and c = -22, we get discriminant (-6)^2 - 4(1)(-22), which evaluates to 36+88 = 124.  124 in turn can be factored:  124 = 4(31).

then:   
       -(-6) plus or minus sqrt( [-6]^2 - 4(1)(-22) )
x =
                                      2
          6 plus or minus 2*sqrt(31)
   =
                              2
     =   3 plus or minus sqrt(31)
   
Note that these are REAL roots, in complete disagreement with the four answer choices.  Please ensure that you have copied the quadratic expression accurately.

Remind yourself that if the discriminant is +, as it is in this case, you have 2 distinct real roots.

The answer would be 27 because assuming that each package has 1 bar of soap and 1 tube of toothpaste, after 27 packages they would run out of toothpaste