Book: RS Aggarwal - Mathematics
Chapter: 10. Quadratic Equations
Subject: Maths - Class 10th
Q. No. 72 of Exercise 10A
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Solve each of the following quadratic equations:
4(x + 1) + 4(1 - x) = 10
Given: 4(x + 1) + 4(1 - x) = 10
- - - - - - - (1)
Let 4x = y - - - - - - - - - - (2)
substituting for y in (1)
4y2 - 10y + 4 = 0
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 = 4 b = - 10 c = 4
= 4.4 = 16
And either of their sum or difference = b
= - 10
Thus the two terms are - 8 and - 2
Sum = - 8 - 2 = - 10
Product = - 8. - 2 = 16
4y2 - 10y + 4 = 0
4y2 - 8y - 2y + 4 = 0
4y(y - 2) - 2(y - 2) = 0
(y - 2) (4y - 2) = 0
(y - 2) = 0 or (4y - 2) = 0
y = 2 or y = 1/2
substituting the value of y in (2)
4x = 2 or 4x = 2 - 1
22x = 21 or 22x = 2 - 1
2x = 1 or 2x = - 1
Hence the roots of equation are 
