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Comparing to this to ax^2 + bx + c = 0, you'll find that a=1, b=-1, c=90. You need to split b (in this case -1), into two numbers that add up to b (-1), and multiply to ac (90). -> These are -10 and 9....

x^2+5x+10 -> (x+p)^2+q (x+5/2)^2 - (5/2)^2 + 10 (x+5/2)^2 - (25/4) +40/4 (x+5/2)^2 +15/4

True probability of 2 consecutive balls picked being blue: (10/30)*(9/29)=3/29 which is 0.1034 (4 d.p.)

3/29-100% 0.2-x% so, x=0.2*100/(3/29)= 193.3 (1 d.p.) therefore Adam's result is 93.3 % (1 d....

The first thing you need to do to make this easier is to multiply out the brackets so that you can then move all the 'x' terms to one side and all the numbers to the other side. It would become: 7x=4x-32 ...

Draw a diagram breaking down 110 and 132 into their multiples (on whiteboard), e.g. 110=1110 132=1112 Circle the prime numbers, 11, and then break down the composite numbers (those that aren't pr...