<p>how do you solve this?</p>
<p>(square root of 2x+13) -1+ square root of x+6</p>
<p>oops- it's </p>
<p>the (square root of 2x+13) -1 = (square root of x+6)</p>
<p>x= -2
Try squaring both sides and see what happens</p>
<p>i am just a mom- I don't know how to do that...please show me</p>
<p>This is not really an SAT type of a question.</p>
<p>To make it slightly easier:
let t = x + 6.
sqrt(2t + 1) - 1 = sqrt(t)
<---- square both sides
2t + 1 - 2sqrt(2t + 1) + 1 = t
<---- isolate the square root, then square both sides again
t + 2 = 2sqrt(2t + 1)
t^2 + 4t + 4 = 8t +4
t(t - 4) = 0
t=0, t=4
x+6=0, x+6=4
x=-6, x=-2.</p>
<p>lol ok, first it would be easier to get the square root symbols by themselves. Do that and you get sqrt(2x+13)-sqrt(x+6)=1
now square both sides and you get
[sqrt(2x+13)-sqrt(x+6)][sqrt(2x+13)-sqrt(x+6)]=1*1
2x+13 +(x+6) -2sqrt([x+6][2x+13])=1
But now we have a sqrt term still so we do it again
isolate the sqrt term
3x+19-2sqrt([x+6][2x+13])=1
-2sqrt([x+6][2x+13])= -3x-18=-3(x+6)
then square both sides again
4(x+6)(2x+13)= 9[x^2+12x+36]
4(x+6)(2x+13)=9(x+6)^2
Now we see we can cancel an (x+6), but note that x=-6 is also a solution, since it's common to both sides
giving us
4(2x+13)=9(x+6)
8x+52=9x+54
so therefore
-2=x
and from the cancellation above, the solutions are
x= -2,-6</p>
<p>So if you're a mom, why would you need to know this anyways?</p>