Question

What are the roots for 3(x+5)^2=27

Answer 1

`x = - 2 \: \: \: \: or \: \: \: \: x = - 8`

Explanation:

`3( {x + 5)}^(2) = 27 \\ \\ {(x + 5)}^(2) = (27)/(3) \\ \\ {x}^(2) + 10x + 25 = 9 \\ {x}^(2) + 10x + 25 - 9 = 0\\ {x}^(2) + 10x + 16 = 0 \\ x { }^(2) + 8x + 2x + 16 = 0 \\ x(x + 8) + 2(x + 8) = 0 \\ (x + 2)(x + 8) = 0 \\ x + 2 = 0 \: \: \: \: or \: \: \: \: x + 8 = 0 \\ x = - 2 \: \: \: \: \: or \: \: \: \: \: x = - 8`

Thus, the roots for 3(x+5)^2=27 is x = -2 or x = -8