# Question #5f8be

##### 3 Answers

#### Explanation:

I remember receiving this problem before . . . Here's how my math teacher explained it:

You can't factor this the way you normally would with quadratic equations, becuase there are no two numbers whose sum is 7 and whose product is 4.

So, you just have to experiment with the problem by inputting factors of

The answer is:

If you FOIL the expression, you'll end up with the original equation.

#### Explanation:

In short, bring over the 4 and factor by grouping

You always have to make the equation equal to zero when factoring so in this case you would bring the 4 over.

NOTE: you can get rid of the zero, it doesn't matter now

Then factor by grouping,

- Multiply the last number by the leading coefficient, in this case 15.

15 * -4 = -60

- Don't replace the - 4 with -60 just find two numbers that add up to -7, but multiplies to -60
- In this case it would be -12 and 5
- Now replace the -
#7x# with -#12# and#5#

NOTE: I placed them the way they are so that when we factor it, it will give us whole numbers

- Then factor by splitting the equation in half
- Factor
#15x^2# #+# #5x# and#-12x# #-# 4 individually - Add brackets to separate them

Now since the numbers are the same you can write it as one, then combine what's outside of the bracket together

(

NOTE: You know you did right if the numbers in the brackets are the same

NORMALLY, you would be done, however the

Therefore,

#### Explanation:

To avoid doing the lengthy factoring by grouping, you may use the new Transforming Method (Socratic, Google Search)

Converted equation:

Proceeding: Find 2 real roots of y', then, divide them by a = 15

The 2 real roots of y' are: - 5 and 12 -->

[Sum = 7 = - b] and Product {ac = - 60]

The 2 real roots of y are: