quick EASY math question ( algebra 2 )?

Question

Ok Im solving quadratic equations and I have the equation

- ( k - 1 ) squared + 7 = - 43

so then I take the square root of ( k -1 ) squared so that it takes away the square of it

I need to know if once I do that, if the negative sign that I started out that was it front of the
(k-1) applies to both the k and the -1 or just the k or just the 1

like is it -k+1=50 or -k-1=50 or k-1=50

I meant for this to be easy but I cant find the square root sign and Im not sure if everyone knows what ^2 means.. I guess you should if you passed or are in algebra 2.. But anyways thanks for any help

Answer 1

You can only take the square root of the whole side, not one term at a time. Proceed as follows:

-(k - 1)² + 7 = -43
-(k - 1)² = -50
(k - 1)² = 50
k - 1 = ±√50 = ±√(25*2) = ±5√2
k = 1 ± 5√2

But k - 1 can't be negative, so the only solution is

k = 1 + 5√2

Answer 2

Well first off, if you take the square root of the left side of the equation you need to do the same thing on the right side of the equation. The first step here is to subtract 7 on both sides so you end up with -(k-1)^2 = -50.
Then, you take the square root of both sides, so you end up with
-k+1= the square root of 50
-k=square root of 50 minus 1
k=square root of 50 plus 1

Answer 3

I think you are trying to make this too complicated but you do understand it :)

- (k-1)squared = -50

the negatives can cancel out and you wind up with the k-1=root 50

or K = (root 50) +1

or k = 8.07

Answer 4

Northstar is wrong. (k-1) can be negative.
The answer is 1 plus or minus 5*sqrt2

Answer 5

the awnser is the square root of 51