# How do you solve #x^2+x-72=0#?

##### 2 Answers

Dec 23, 2015

Find a pair of factors of

#x^2+x-72 = (x+9)(x-8)#

which has zeros

#### Explanation:

In general

In our case we want

It should not take long to find that

Dec 23, 2015

Complete the square to find zeros

#### Explanation:

Alternatively, complete the square as follows:

Note that

We also use the difference of squares identity:

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

with

So:

#x^2+x-72#

#= x^2+x+1/4-1/4-72 = (x+1/2)^2-289/4#

#= (x+1/2)^2-(17/2)^2#

#= ((x+1/2)-17/2)((x+1/2)+17/2)#

#= (x-8)(x+9)#

which has zeros