# How do you solve t - sqrt (6t - 9) = 0?

Feb 5, 2016

$t = 3$

#### Explanation:

Given: $t - \sqrt{6 t - 9} = 0$.......................(1)

Things would be easier if we 'got rid' of the square root!

$t = \sqrt{6 t - 9}$

Square both sides

${t}^{2} = 6 t - 9$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Make into a quadratic equation

${t}^{2} - 6 t + 9 = 0$

Observe that$\text{ " -3-3=-6 " and that } \left(- 3\right) \times \left(- 3\right) = + 9$

Factorising gives:

${\left(t - 3\right)}^{2} = 0$

so$\text{ } t = + 3$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Check if correct!

Substituting for t in equation 1 and consider the left hand side only

$3 - \sqrt{6 \left(3\right) - 9}$

$3 - \sqrt{18 - 9}$

$3 - \left(\pm 3\right)$

The only possible value for the LHS to be zero is to have:

$L H S \to 3 - 3 = 0 \text{ and } R H S \to 0$ so proven to be correct