Question

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

Answer 1

`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`