my problem is
square root (a+21)-1= square root(a+12) I am kind of stuck on how to solve this as I do not know what to do with -1.
Also the next equation I need help solving is very similar
sqrt (x+2)-7= square root (x+9) Can anyone please help me?
my problem is
square root (a+21)-1= square root(a+12) I am kind of stuck on how to solve this as I do not know what to do with -1.
Also the next equation I need help solving is very similar
sqrt (x+2)-7= square root (x+9) Can anyone please help me?
$\displaystyle \sqrt{a+21}-1=\sqrt{a+12}$
$\displaystyle (\sqrt{a+21}-1)^2=(\sqrt{a+12})^2$
$\displaystyle a+21 - 2\sqrt{a+21} + 1 = a+12$
Use algebra to get $\displaystyle \sqrt{a+21}$ on one side. Once you do that, you can square both sides and no more square roots. Now you can solve for $\displaystyle a$. It will be a quadratic equation.
Note: Remember once you get a solution, plug it back in to check. Especially for square root problems, you can get extra "fake" solutions. Always plug in and check.
No, you add $\displaystyle 2\sqrt{a+21}$ to both sides.
You cancel $\displaystyle -2\sqrt{a+21}$ from the side it's on.
If two sides are equal, then if you add the same thing to both sides, they will still be equal.
As in.... 5=5, 5+2=5+2 or 5-2=5-2 etc
therefore
$\displaystyle a+22-2\sqrt{a+21}=a+12$
Add $\displaystyle 2\sqrt{a+21}$ to both sides and then subtract $\displaystyle (a+12)$ from both sides.
Alternatively, subtract $\displaystyle (a+22)$ from both sides.
Then divide both sides by $\displaystyle -2$ and square both sides.
You could also go this route...
$\displaystyle \displaystyle\sqrt{a+21}-1=\sqrt{a+12}$
$\displaystyle \displaystyle\sqrt{\left(\sqrt{a+21}-1\right)^2}=\sqrt{a+12}$
$\displaystyle \displaystyle\sqrt{a+21-2\sqrt{a+21}+1}=\sqrt{a+12}$
$\displaystyle \sqrt{a+22-2\sqrt{a+21}}=\sqrt{a+12}$
$\displaystyle a+22-2\sqrt{a+21}=a+12$
$\displaystyle a+12+10-2\sqrt{a+21}=a+12$
which means that
$\displaystyle 10-2\sqrt{a+21}=0$
If two values are equal, when we subtract them the answer is zero...
$\displaystyle 10=2\sqrt{a+21}\Rightarrow\sqrt{a+21}=5\Rightarrow \ a+21=25$
If $\displaystyle A=\sqrt{a+21}\Rightarrow\ A^2=a+21\Rightarrow\ a+12=A^2-9$
Then....
$\displaystyle \left[\sqrt{a+21}\right]^2-2\sqrt{a+21}+1=a+12$
$\displaystyle A=\sqrt{a+21}$
$\displaystyle A^2-2A+1=A^2-9$
$\displaystyle -(2A-1)=-9$
$\displaystyle 2A-1=9$
$\displaystyle A=5\Rightarrow\sqrt{a+21}=\sqrt{25}\Rightarrow\ a+21=25$