Question

How to solve a quadratic equation by spreading middle term?

And I want to know that how to spread middle term and solve a equation..

Answer 1

Consider, 7x2 – 98x + 336 = 0
First find the product of 7x2 and 336, we get 2352x2
Now notice that we have a negative sign in the middle term
Hence we have to split this into two negative numbers such that its product is positive this is because the product of 1st and last obtained is positive (2352x2).
Also notice that the last digit in 2352x2 is 2 so the one of the two numbers should end with 2 and other with 6.
Consider the product of 56 and 42 which is 2352
Hence 7x2 – 98x + 336 = 0 can be written as 7x2 – 56x – 42x + 336 = 0
⇒ 7x(x – 8) – 42(x – 8) = 0
⇒ (x – 8)(7x – 42) = 0
⇒ (x – 8) = 0 or (7x – 42) = 0
⇒ x = 8 or x = 6