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

Jun 17, 2015

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

#### Explanation:

${\left(a + 15\right)}^{2} = 400$

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

${\left(a + 15\right)}^{2} = {a}^{2} + 2. \left(15\right) . a + {15}^{2}$
 = color(blue)(a^2 + 30a + 225

Our expression now becomes :
$\textcolor{b l u e}{{a}^{2} + 30 a + 225} = 400$
${a}^{2} + 30 a - 175 = 0$

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

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