# What is the new Transforming Method to solve quadratic equations?

##### 1 Answer

Solving quadratic equations by the new Transforming Method

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#### Explanation:

**Case 1** . Equation type:

Find 2 numbers knowing sum (-b) and product (c). Compose factor pairs of c, and in the same time apply the Rule of Signs. Find the factor pair that equals to b, or (-b).

Example 1. Solve

Roots have opposite signs. Factor pairs of (-102)--> ...(-2, 51)(-3, 34)(-6, 17). This sum is 11 = -b. Then, the 2 real roots are: -6 and 17.

Example 2. Solve

Both roots are positive, Factor pairs of 126 --> ...(2, 63)(3, 42)(6, 21). This sum is 27 = -b. Then, the 2 real roots are: 6 and 21

**Case 2** . Equation standard type:

Transformed equation:

Solve the equation (2) exactly like in Case 1. Find its 2 real roots y1 and y2. Next, find the 2 real roots of the original equation (1) by these relations:

Example 3. Solve

Transformed equation:

Back to original equation (1), the 2 real roots are:

Example 4. Solve

Transformed equation:

NOTE. This method is fast, systematic, no guessing, no lengthy factoring by grouping.