# How do you solve x – 3sqrtx = 10 ?

##### 1 Answer
Jul 19, 2016

$x - 10 = 3 \sqrt{x}$

${\left(x - 10\right)}^{2} = {\left(3 \sqrt{x}\right)}^{2}$

${x}^{2} - 20 x + 100 = 9 x$

${x}^{2} - 29 x + 100 = 0$

$\left(x - 25\right) \left(x - 4\right) = 0$

$x = 25 \mathmr{and} 4$

Checking back in the initial equation, we find that only $x = 25$ works. Hence, the solution set is $\left\{25\right\}$.

Hopefully this helps!