<PRE><B>Question 288376</B>
I need to solve this radical equation using the power principle.
Problem: {{{sqrt(x+7)-2=sqrt(x-9)}}}
I can work the other problems pretty easily, but they all have numbers before the x (ie {{{sqrt(2x-9)}}}, so I can understand them a little better.
This one is throwing me for a loop.
I tried,
{{{sqrt(x+7)=2+sqrt(x-9)}}}
and got
{{{(sqrt(x+7))^2=(2+sqrt(x-9))^2}}}
When you FOILed the right side, you should get
x + 7 = {{{4 + 4sqrt(x-9) + (x-9)}}}
:
x + 7 = {{{x - 5 + 4sqrt(x-9))}}}
:
x - x + 7 + 5 = {{{4sqrt(x-9)}}}
:
12 = {{{4sqrt(x-9)}}}
:
Square both sides and you have
144 = 16(x-9)
Divide both sides by 16
9 = x - 9
9+9 = x
x = 18
;
:
Check solution in original problem
{{{sqrt(18+7)-2=sqrt(18-9)}}}
{{{sqrt(25)-2=sqrt(9)}}}
</PRE>