# How to compare the AC Method (factoring by grouping) and the new Transforming Method in solving quadratic equations?

##### 2 Answers

Solving quadratic equations by the new Transforming Method

#### Explanation:

A good way to compare these 2 methods is solving a sample of quadratic equation.

The Transforming Method. Solve

Transformed equation:

Proceeding: Find the 2 real roots of the transformed equation y', then, divide them by a = 16.

Find 2 numbers knowing sum (-b = 62) and product (ac = 336).

Compose factor pairs of (336) --> ...(4, 82)(6, 56). This sum is (6 + 56 = 62 = -b). Then, the 2 real roots of y' are: 6 and 56.

Back to y, the 2 real roots are:

Solving quadratic equation by the AC Method (splitting the middle term)

#### Explanation:

Proceed to split the middle term by proceeding as follows:

Find 2 numbers knowing sum (b = -62) and product

(ac = 16*21 = 336)

Compose factor pairs of (336):

... (-4, - 82)(-6, -56). This sum is (-62) and its product is (336).

Re-write the equation and split the middle term (-62x) into (-6x) and

(- 56x)

Solve the 2 binomials:

NOTE. The new Transforming Method (Google Search) avoids the lengthy factoring by grouping and solving the 2 binomials.

After you find the 2 numbers (-6) and (-56). Take the opposite of them, (6) and (56), then divide them by a = 16, you immediately get the 2 real roots. You don't need to proceed factoring by grouping further.