Question

What are the solutions of the equation (x + 2)2 – 2(x + 2) – 15 = 0? Use u substitution to solve. x = –7 and x = 1 x = –5 and x = 3 x = –3 and x = 5 x = –1 and x = 7

Answer 1

The given equation is

$(x+2)^2 -2(x+2)-15=0$

$let \ u \ = \ x+2$

So we will get

$u^2 -2u-15=0$

Factoring the left side

$(u-5)(u+3)=0$

$u-5=0, u +3 =0$

Solving both equations for u

$u= 5, -3$

Performing back substitution

$x+2 = 5, x+2 =-3 \\ x = 3, -5$

And that's the required solutions .

Answer 2

Answer:

B.) x = –5 and x = 3