Triangle GHI is a right triangle; GH=5, HI= x+4, GI= 2x-3

[Karashii]

find all possible values of X.


I got x=8, thats not the only answer right?

so I tried: GH (squared) * GI (squared), and got-

3x(squared)-20x+18=0

I can't seem to factor it though =[

Please help?

 

[arthur ohlsten]

gh=5
gi=2x-3 x> 1.5 for positive gi
hi=x+4 x>-4

a)
5^2=[2x-3]^2+[x+4]^2
25= 4x^2-12x+9 +x^2+8x+16
0=5x^2-4x
0=x[5x-4]
x=0 or x=.8 extraneous solution

b)
[2x-3]^2=5^2+[x+4]^2
4x^2-12x+9=25 +x^2+8x+16
3x^2-20x-32=0
[3x+4][x-8]=0
x=-4/3 extraneous
x=8 answer

c)
[x+4]^2=5^2+[2x-3]^2
x^2+8x+16=25+[4x^2-12x+9]
0=3x^2-20x+18
x=20+/-[400 -216]^1/2 all over 6
x=20+/-[184]^1/2 all over 6
x=10+/-[46]^1/2 all over 3
x=[10+sqrt46 ] / 3 answer
x=[10-sqrt46] /3 answer

please check for errors
Arthur