OpenStudy (anonymous):

how can I solve -(x+5)^2 + 9 ?

OpenStudy (anonymous):

ah! should be -(x-5)^2 + 9. I distributed the square and got x^2 + 34, but how do you factor that?

OpenStudy (jim_thompson5910):

you made the mistake in thinking that (x-5)^2 = x^2 + 25 when in fact it should be (x-5)^2 = x^2 - 10x + 25

OpenStudy (jim_thompson5910):

so -(x-5)^2 = -(x^2 - 10x + 25) -(x-5)^2 = -x^2 + 10x - 25

OpenStudy (anonymous):

oh! so -x^2 + 10x -16 and then you continue to factor it...

OpenStudy (jim_thompson5910):

correct

OpenStudy (anonymous):

(-x^2-2)+ (8x-16) ?

OpenStudy (anonymous):

the negatives are confusing....

OpenStudy (jim_thompson5910):

-x^2 + 10x - 16 -(x^2 - 10x + 16) now factor x^2 - 10x + 16 and when you're done factoring, stick a negative at the front

OpenStudy (anonymous):

whoops, should it be (x+2) (x-8), or x equals +/- 2, +/- 8 ?

OpenStudy (jim_thompson5910):

x^2 - 10x + 16 factors to (x-2)(x-8) so -(x^2 - 10x + 16) factors to -(x-2)(x-8)

OpenStudy (jim_thompson5910):

-(x^2 - 10x + 16) = 0 -(x-2)(x-8) = 0 x-2 = 0 or x -8 = 0 x = 2 or x = 8

OpenStudy (jim_thompson5910):

you won't have the plus or minus

OpenStudy (anonymous):

oh, ok. thank you!

OpenStudy (jim_thompson5910):

sure thing