when anybody tend to solve any Quadratic equation, the first method which comes in his or her mind is solving that equation by MTS method.

standard form of Quadratic equation is

i.e. first term or the highest degree of equation must be 2, then a linear term and then constant term should be arranged.
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Middle term Splitting Method

**MTS means Middle term splitting.**

standard form of Quadratic equation is

**ax² + bx + c**

i.e. first term or the highest degree of equation must be 2, then a linear term and then constant term should be arranged.

here Middle term is

**bx**, this should be splitted.###
- How To Apply MTS –

MTS means middle term should be splitted,

But the question us HOW???

### Here is the answer cum method step by step –

*Multiply 1st and the last numbers, put this aside.**Now pick the middle term and try to split this into two parts such that when those terms added/subtracted the resultant should be the, same middle term and when those terms are multiplied the resultant should be equal to the resultant which occurred in first step.**That’s why this method is known as MTS.**Now we’ll have four terms, among those four terms make the group of first two and last two.**Take the common out from those groups.**Do remember..!!**After taking common out the values in the Brackets should be equal otherwise this may become sign of wrong solution.**Now we’ll have two brackets take one and form an another bracket using values which were lying outside the Brackets.**Finally we’ll have two Brackets which are the required factorisation of given equation.*

Check this image based solutions

For an example :-

x² + 5x + 6

multiplying 1st and last term x² × 6 = 6x²

Splitting 5x

2x and 3x can be splitting terms

as 2x + 3x = 5x

and 2x × 3x = 6x²

hence

x² + 5x + 6

x² + 2x + 3x + 6

by grouping

(x² + 2x ) + ( 3x + 6)

taking common out

x ( x + 2) + 3 ( x + 2)

do remember brackets are similar hence we are proceeding correctly

final step

( x+ 2) ( x+ 3)

ans.

- Further more if we are to ask to find the factors of the equation also.

Then We have to apply MTS first and have to find brackets as well then these brackets individually give factors respectively for this purpose see below –

now

(x +2 ) ( x + 3) = 0

either ( x+ 2) = 0 ; x = -2

or ( x + 3) = 0 ; x = -3

- See video for better understanding.
- Try another method
- Try Completing the square method to solve quadratic equations