# How do you solve #m^2 + 8m + 15 = 0# by completing the square?

##### 1 Answer

Apr 2, 2016

Complete the square to find

#### Explanation:

Note that:

#(m+4)^2 = m^2+2(m)(4) + 4^2 = m^2+8m+16#

So add

#m^2+8m+16 = 1#

which we can write as:

#(m+4)^2 = 1#

Then take the square root of both sides, allowing for both positive and negative square roots to find:

#m+4 = +-sqrt(1) = +-1#

Subtract

#m = -4+-1#

That is

**Alternative method**

Use the difference of squares identity:

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

with

#0 = m^2+8m+15#

#= (m+4)^2-16+15#

#= (m+4)^2-1#

#= (m+4)^2 - 1^2#

#= ((m+4) - 1)((m+4) + 1)#

#= (m+3)(m+5)#

So