Math Help - 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

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

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

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

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

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

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

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

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

square to give:
$
125=x^2+8x+116
$

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