Question

What are the solutions of the equation (x + 2)^2+ 12(x + 2)-14=0? Use u substitution and the quadratic formula to solve

Answer 1

Explanation:

Obviously, we are letting u = x + 2. So what we have when we rewrite using this substitution is

`u^2+12u-14=0` and we plug that into the quadratic formula with

a = 1, b = 12, c = -14:

`u=(-12+-√(12^2-4(1)(-14)) )/(2(1))` which can be simplified to

`u=(-12+-√(144+56) )/(2)` and a bit more to

`u=(-12+-√(200) )/(2)` and a tiny bit more to

`u=(-12+-10√(2) )/(2)` and finally to

`u=-6+-5√(2)` and plug back in for u:

x + 2 = -6 ± 5√2 and then subtract the 2 to get

x = -8 ± 5√2