Question 885250
To find x we need to find the distance between A and B and the distance between B and C.  We can then set the two distances equal to each other and solve for x, since AB=BC.<br>

So finding the distance between A and B we get:<br>

{{{AB=sqrt((x2-x1)^2+(y2-y1)^2)}}}
{{{AB=sqrt((-3-x)^2+(2-3)^2)}}}
{{{AB=sqrt(x^2+6x+9+(-1)^2)}}}
{{{AB=sqrt(x^2+6x+9+1)}}}
{{{AB=sqrt(x^2+6x+10)}}}<br>

That's as simplified as that can get.  So now we find the distance between B and C:<br>

{{{BC=sqrt((x2-x1)^2+(y2-y1)^2)}}}
{{{BC=sqrt((x-4)^2+(3-5)^2)}}}
{{{BC=sqrt(x^2-8x+16+(-2)^2)}}}
{{{BC=sqrt(x^2-8x+16+4)}}}
{{{BC=sqrt(x^2-8x+20)}}}<br>

So now we can set AB = BC and solve for x.

{{{sqrt(x^2+6x+10)}}} = {{{sqrt(x^2-8x+20)}}} square both sides to get rid of the square root

{{{x^2+6x+10 = x^2-8x+20}}} Subtract (x2-8x+20) from both sides
{{{x^2-x^2+6x+8x+10-20 = 0}}} combine like terms
{{{14x-10 = 0}}} add 10 to both sides
{{{14x = 10}}} divide both sides by 14
x = 10/14 = 5/7