Had Aarush scored 8 more marks in a Mathematics test . . .

Question : Had Aarush scored 8 more marks in a Mathematics test, out of 35 marks, 7 times these marks would have been 4 less than square of his actual marks. How many marks did he get in the test?

Doubt by CBSE

Solution : 

Let the original marks obtained by Aarush in the test be x.
ATQ

7(x+8)=x²-4

7x+56=x²-4

0=x²-4-7x-56

0=x²-7x-60
x²-7x-60=0

x²-(12-5)x-60=0
[∵ Splitting the middle term]

x²-12x+5x-60=0

x(x-12)+5(x-12)=0

(x+5)(x-12)=0
x+5=0 OR x-12=0
x=-5 OR x=12

∵ Marks can't be negative.
∴ x≠-5

so, x=12

Hence, original marks obtained by Aarush in the test is 12.