SOLUTION: h^2+28h-3=0

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Question 788114: h^2+28h-3=0
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
I see two ways to solve h%5E2%2B28h-3=0.

COMPLETING THE SQUARE:
h%5E2%2B28h-3=0
h%5E2%2B28h=3
Here we notice that h%5E2%2B28h is part of h%5E2%2B28h%2B196=h%5E2%2B28h%2B14%5E2=%28h%2B14%29%5E2
h%5E2%2B28h%2B196=3%2B196
%28h%2B14%29%5E2=199
So h%2B14=sqrt%28199%29 or h%2B14=sqrt%28199%29,
which can be summarized as
h=-14+%2B-+sqrt%28199%29

APPLYING THE QUADRATIC FORMULA:
An equation of the form ax%5E2%2Bbx%2Bc=0 has solutions given by
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
as long as b%5E2-4%2Aa%2Ac%3E=0 (because otherwise sqrt%28+b%5E2-4%2Aa%2Ac%29 does not exist).
In the case of h%5E2%2B28h-3=0
x=h, a=1, b=28, and c=-3, so
x+=+%28-28+%2B-+sqrt%28+28%5E2-4%2A1%2A%28-3%29+%29%29%2F%282%2A1%29+
x+=+%28-28+%2B-+sqrt%28784%2B12+%29%29%2F2+
x+=+%28-28+%2B-+sqrt%28796%29%29%2F2+
x+=+%28-28+%2B-+sqrt%284%2A199%29%29%2F2+
x+=+%28-28+%2B-+sqrt%284%29%2Asqrt%28199%29%29%2F2+
x+=+%28-28+%2B-+2sqrt%28199%29%29%2F2+
x+=+-14+%2B-+sqrt%28199%29+