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

##### 1 Answer

Mar 14, 2016

See explanation...

#### Explanation:

I will use the difference of squares identity:

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

with

If I see an odd middle coefficient and am asked to "complete the square", I tend to groan slightly inwardly at the prospect of messy fractions.

Happily we can avoid some of the mess by multiplying our equation through by

#0 = 4(x^2+5x-6)#

#=4x^2+20x-24#

#=(2x+5)^2-25-24#

#=(2x+5)^2-49#

#=(2x+5)^2-7^2#

#=((2x+5)-7)((2x+5)+7)#

#=(2x-2)(2x+12)#

#=4(x-1)(x+6)#

So the roots are: