^{2}and x

^{0}. So, let us understand how this approach works for quadratic equations through an example:

Example: How do you solve 7x to the power 2 plus 3x minus 4 equal to 0?

Solution: Quadratic equation that has been given to us is of the form:

7x

^{2}+ 3x – 4 = 0,

When this equation is compared to general equation of a Quadratic Equation i.e. Ax

^{2}+ B x + C = 0, we see that:

A = 7,

B = 3 and,

C = - 4,

On multiplying A and C we get 7 * -4 = - 28.

Now to use mid - term splitting technique we first check for two Numbers such that their product is -28 and their difference or addition is 3. We see that 7 and – 4 would result into respective product and difference. So, we can split middle term as follows:

7 x

^{2}+ 3x – 4 = 0,

7 x

^{2}+ 7x – 4x – 4 = 0,

Factorizing the above equation:

7x (x + 1) – 4 (x + 1) = 0,

Or (x + 1) (7 x – 4) = 0,

Or x + 1 = 0 and 7x – 4 = 0,

Or x = - 1 and x = 4 /7,

Thus we get two roots for equation as x = - 1 and x = 4 /7.