How do you solve #(a+15)^2 = 400#?

1 Answer
Jun 17, 2015

Answer:

# color(red)( a = 5, a =-35#

Explanation:

#(a+15)^2 = 400#

Applying identity : #color(blue)((a+b)^2= a^2 + 2ab +b^2#

#(a+15)^2 = a^2 + 2.(15).a + 15^2#
# = color(blue)(a^2 + 30a + 225#

Our expression now becomes :
# color(blue)(a^2 + 30a + 225) = 400#
# a^2 + 30 a -175 = 0#

We can now first factorise this expression and thereby find the solutions:
Factorising by splitting the middle term
# a^2 + 30 a -175 = 0#
# a^2 + 35a - 5 a -175 = 0#
# a(a + 35) - 5( a + 35) = 0#

# (a - 5)(a + 35) = 0#
Upon equating the factors with zero we obtain the solutions as :
# color(red)( a = 5, a =-35#