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

1 Answer
Don't Memorise
Jun 17, 2015

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

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