got 2 answers, 1 makes no sense x(x+1)^3 - 42(x+1)^2 = 0

[mrnerd]

I got the 2 obvious answers I think:
x(x + 1)^3 - 42(x + 1)^2 = 0

x(x + 1)^3 = 42(x + 1)^2

x(x + 1) = 42

(x + 1/2)^2 = 169/4

x + 1/2 = +- 13/2

x = 6, x = -7
This is my work so far, and the book says I'm correct. However there is an additional answer x = -1, and I don't understand where that comes from
Thanks

 

[Deleted member 4993]

I got the 2 obvious answers I think:
x(x + 1)^3 - 42(x + 1)^2 = 0

x(x + 1)^3 = 42(x + 1)^2

x(x + 1) = 42

(x + 1/2)^2 = 169/4

x + 1/2 = +- 13/2

x = 6, x = -7
This is my work so far, and the book says I'm correct. However there is an additional answer x = -1, and I don't understand where that comes from
Thanks

Your problem should be done the following way:

x(x + 1)^3 - 42(x + 1)^2 = 0

(x+1)^2 * [x(x+1)-42] = 0

(x+1)^2 * (x+7) * (x-6) = 0

The equation above will be satisfied when:

(x+1)^2 = 0 → x = -1

x + 7 = 0 → x = -7

x - 6 = 0 → x = 6

Now you need to think why your method gave you incomplete answer!

 

[Harry_the_cat]

I got the 2 obvious answers I think:
x(x + 1)^3 - 42(x + 1)^2 = 0

x(x + 1)^3 = 42(x + 1)^2

x(x + 1) = 42 Here you have divided both sides by (x+1)^2. But you can't do that if (x+1)^2=0. You need to use a factorising method (see reply above). Otherwise you could "lose" a solution as you have done here.

(x + 1/2)^2 = 169/4

x + 1/2 = +- 13/2

x = 6, x = -7
This is my work so far, and the book says I'm correct. However there is an additional answer x = -1, and I don't understand where that comes from
Thanks

See green comment

 

[mrnerd]

thanks so much guys, I guess I didn't realize that you could factor out (x + 1) like that in the (x + 1)^3 - 42(x + 1)^2 expression. It seems so obvious now.
Thanks again!