Solve equations $\sqrt{t +9} - \sqrt{t} = 1$ Solve equation:  $\sqrt{t +9} - \sqrt{t} = 1$
I moved - √t to the left side of the equation $\sqrt{t +9} = 1 -\sqrt{t}$
I squared both sides $(\sqrt{t+9})^2  = (1)^2 (\sqrt{t})^2$
Then I got $t + 9 = 1+ t$
Can't figure it out after that point.
The answer is $16$

An often overlooked fact is that
$$ \sqrt{t^2}=\left|t\right|$$
Call me paranoid but here's how I would solve this
$$\sqrt{t +9} - \sqrt{t} = 1$$
$$\sqrt{t +9}  = \sqrt{t}+1$$
$$\left|t +9\right|  = \left(\sqrt{t}+1\right)\left(\sqrt{t}+1\right)$$
$$\left|t +9\right|  = \left|t\right|+2\sqrt{t}+1$$
Since the original equation has $\sqrt{t}$, then we know that $t\geq 0$ and we can safely remove the absolute value bars. So now we have
$$t +9= t+2\sqrt{t}+1$$
$$9= 2\sqrt{t}+1$$
$$8= 2\sqrt{t}$$
$$4= \sqrt{t}$$
$$\left|t\right|=4^2$$
$$t=16$$
