# How do you solve #3q^2 - 16q = -5#?

##### 3 Answers

May 1, 2017

shift everything to one side to give a quadratic equation

#### Explanation:

May 1, 2017

#### Explanation:

substitute

substitute

May 24, 2017

#### Explanation:

There are 2 methods to choose:

- The AC Method --> split the middle term for factoring:

Find 2 numbers knowing sum (b = -16) and product (ac = 15).

They are -1 and - 15.

Split - 16q into -q and - 15q

#y = 3q^2 - q - 15q + 5 = q(3q - 1) - 5(3q - 1) = (3q - 1)(q - 5)#

(3q - 1) = 0 --> 3q = 1 -->#q = 1/3#

q - 5 = 0 --> q = 5 - The New Transforming Method (Socratic Search)

#y = 3q^2 - 16q + 5 = 0#

Transformed equation:

#y' = q^2 - 16q + 15 = 0#

Method: Find the 2 real roots of y', then divide them by a = 3

Find 2 numbers (real roots) knowing sum (-b = 16) and product (ac = 15). They are: 1 and 15.

Back to y, the 2 real roots are:#x1 = 1/a = 1/3,# and#x 2 = 5/a = 5/3#