# How do you solve sqrt( t - 9) - sqrtt = 3?

Mar 14, 2018

See below...

#### Explanation:

First we need to manipulate the equation to get $t$ by itself.

$\sqrt{t - 9} - \sqrt{t} = 3$
$\sqrt{t - 9} = 3 + \sqrt{t}$

Now let's expand both sides to remove the root.

${\sqrt{t - 9}}^{2} = {\left(3 + \sqrt{t}\right)}^{2}$
$t - 9 = 9 + 6 \sqrt{t} + t$

Now by manipulating this equation we can solve for $t$

$t - 18 = 6 \sqrt{t} + t$
$- 18 = 6 \sqrt{t}$
${\left(- 18\right)}^{2} = \left(6 \sqrt{t}\right) 2$
$324 = 36 t$
$t = 9$

Now we have to verify the solution by subbing $t$ back into the original equation.

$\sqrt{9 - 9} - \sqrt{9} = 3$
$0 - 3 = 3$
$- 3 = 3$

This is false, $\therefore$ no actual solutions.