If line segment PQ is congruent to line segment RS, and `PQ= x ^2-5` , and `RS = 2x+3` , then find PQI solved it out and set PQ equal to RS and factored it and got x= -2 and 4. But, when you plug...

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...

Expert Answers
lemjay eNotes educator| Certified Educator

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.

          `PQ=RS`

        `x^2-5=2x+3`

 `x^2-2x-8=0`

Factor left side.

`(x-4)(x+2)=0`

Set each factor to zero and solve for x.

`x-4=0`                   and               `x+2=0`

   `x=4`                                            `x=-2`

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.