SOLUTION: Two lines have slopes 2k-4 and k+6. What value(s) of k will produce perpendicular lines? I think the answer is k=-4+ or - sqrt62/2???

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Question 132777: Two lines have slopes 2k-4 and k+6. What value(s) of k will produce perpendicular lines? I think the answer is k=-4+ or - sqrt62/2???
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The slopes need to have the relation m%5B1%5D+=+-+1%2Fm%5B2%5D
where m%5B1%5D+=+2k+-+4
and m%5B2%5D+=+k+%2B+6
2k+-+4+=+-%281%2F%28k+%2B+6%29%29
%282k+-+4%29%28k+%2B+6%29+=+-1
2k%5E2+%2B+8k+-+24+=+-1
2k%5E2+%2B+8k+-+23+=+0
k+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
k+=+%28-8+%2B-+sqrt%28+8%5E2-4%2A2%28-23%29+%29%29%2F%282%2A2%29+
k+=+%28-8+%2B-+sqrt%28+248+%29%29%2F4+
k+=+-2+%2B-+%28sqrt%2862%29%29%2F2