# Thread: Distance Formula with given Distance but not X!

1. ## Distance Formula with given Distance but not X!stil needs help!

okay, the question is...
18. The distance between point A and B is 5times Squareroot 5 units. If point A is -4,-7 and point B is x,3 whats the X?

i think ur supposed to put it in standard form but ive tried it but i got confused and didnyt know what to do next

oh and i plugged everything into the distance formula and guessed that x is 1 and it worked but i want to why its 1 and stuffs

2. Originally Posted by sacred3
okay, the question is...
18. The distance between point A and B is 5times Squareroot 5 units. If point A is -4,-7 and point B is x,3 whats the X?

i think ur supposed to put it in standard form but ive tried it but i got confused and didnyt know what to do next

oh and i plugged everything into the distance formula and guessed that x is 1 and it worked but i want to why its 1 and stuffs
You just must solve

$\displaystyle 5\sqrt{5}=\sqrt{(x+4)^2+100}$

3. how did u get x+4? i thought its -4 -x( sorry im not that good at math)

4. Originally Posted by sacred3
how did u get x+4? i thought its -4 -x( sorry im not that good at math)
No problem whatsoever! They are equivalent in this case.

Consider that

$\displaystyle \left(-x-4\right)^2=\left(-(x+4)\right)^2=(-1)^2\cdot(x+4)^2=(x+4)^2$

5. for x+4 squared can i do x squared +16?

cuz then i dont know what to do with
$\displaystyle (x+4)^2$

6. $\displaystyle (x+4)^2 = x(x + 4) + 4(x + 4) = x^2 + 4x + 4x + 16 = x^2 + 8x + 16$

Distribute each term separately and then add them together.

7. im stuck :[

8. please someone help me this is due tomorow and im REALLY STUCK!

9. ive done everythng and ive got my C = -9 and i dont know what to do HELP! or jsut gimme answer and tell me why ! i need it for tommorrow!! HELP PLEASE!

10. $\displaystyle 5\sqrt{5}=\sqrt{(x+4)^2+100}$

so:
$\displaystyle 5\sqrt{5}=\sqrt{x^2+8x+16+100}=\sqrt{x^2+8x+116}$

square to give:
$\displaystyle 125=x^2+8x+116$
then:
$\displaystyle x^2+8x-9=0$
factorise to get
$\displaystyle (x+9)(x-1)=0$
so the two solutions of x are x=1 and x=-9.