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- sqrt66/2????????

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Question 132645: 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- sqrt66/2????????
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
Their slopes will be perpendicular when their product is -1. So we have the equation

Foil

Add 1 to both sides

Let's use the quadratic formula to solve for k:

Starting with the general quadratic

the general solution using the quadratic equation is:

So lets solve ( notice , , and )

Plug in a=2, b=8, and c=-23

Square 8 to get 64

Multiply to get

Combine like terms in the radicand (everything under the square root)

Simplify the square root (note: If you need help with simplifying the square root, check out this solver)

Multiply 2 and 2 to get 4

So now the expression breaks down into two parts

or

Now break up the fraction

or

Simplify

or

So these expressions approximate to

or

So our solutions are:
or