# How do you solve using the completing the square method #3x^2-5x-6=0#?

##### 1 Answer

May 10, 2016

#### Explanation:

Use the difference of squares identity:

#a^2-b^2=(a-b)(a+b)#

with

To avoid too much arithmetic with fractions, pre-multiply the equation by

#0 = 12(3x^2-5x-6)#

#=36x^2-60x-72#

#=(6x-5)^2-5^2-72#

#=(6x-5)^2-25-72#

#=(6x-5)^2-97#

#=(6x-5)^2-(sqrt(97))^2#

#=((6x-5)-sqrt(97))((6x-5)+sqrt(97))#

#=(6x-5-sqrt(97))(6x-5+sqrt(97))#

#=36(x-5/6-sqrt(97)/6)(x-5/6+sqrt(97)/6)#

So