Question

How do you solve `a^2-2a-224=0`?

Answer 1

Solve `y = x^2 - 2x - 224 = 0`

Explanation:

`y = x^2 - 2x - 224 = 0`.
I use the new Transforming Method (Google Yahoo Search)
Find 2 numbers knowing sum (2) and product (-224). Roots have different signs.
Factor pairs of (-224) -> ...(-8, 28)(-14, 16). This sum is 2 = -b. Then, the 2 real roots are: `- 14 and 16.`

Answer 2

Factor the trinomial as the product of two binomials. Set each binomial equal to zero, and solve for `a`.

Explanation:

`a^2-2a-224=0`

Find two numbers that when added equal `-2`, and when multiplied equal `-224`. The numbers `-16` and `14` fit the pattern.

`a^2-2a-224=0` =

`(a-16)(a+14)=0`

Set `(a-16)` equal to zero and solve for `a`.

`a-16=0`

#a=16

Set `(a+14)` equal to zero and solve for `a`.

`a+14=0`

`a=-14`

`a=16, -14`