If line segment PQ is congruent to line segment RS, and `PQ= x ^2-5` , and `RS = 2x+3` , then find PQ
I solved it out and set PQ equal to RS and factored it and got x= -2 and 4. But, when you plug either one back into the equation for PQ, it turns out negative and you can't have a negative measure for a line segment...
Your solution is correct. Let's try to do it again to clarify.
Since PQ and RS are congruent, to solve for x, set PQ=RS.
Factor left side.
Set each factor to zero and solve for x.
`x-4=0` and `x+2=0`
Substitute the values of x to PQ and RS.
`x=4` , `PQ=4^2-5=11` and `RS=2(4)+3=11`
`x=-2` , `PQ=(-2)^2-5=-1` and `RS=2(-2)+3=-1`
Since PQ and RS represents the length of the line segment, then take only the positive values.
Hence, PQ=RS=11 units.