Book: RS Aggarwal - Mathematics
Chapter: 10. Quadratic Equations
Subject: Maths - Class 10th
Q. No. 12 of Exercise 10A
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12
Solve each of the following quadratic equations:
x2 = 18x – 77
Using the splitting middle term - the middle term of the general equation 
is divided in two such values that:
Product = a.c
For the given equation a = 1; b = -18; c = 77
= 1.77 = 77
And either of their sum or difference = b
= - 18
Thus the two terms are - 7 and - 11
Sum = - 7 - 11 = - 18
Product = - 7. - 11 = 77
x(x-7)-11(x-7) = 0
(x-7)(x-11) = 0
(x-7) = 0 or (x-11) = 0
x = 7 or x = 11
Roots of equation are 7, 11
