# How do you solve 3sqrtx + x = 10?

Jun 24, 2016

$x = 4$

#### Explanation:

'Transpose' $x$ to the other side of the equation and square both sides.
Expand the binomial on the right side.
'Transpose $9 x$ to the right side of the equation.

It should look like this:

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

$9 x = {\left(10 - x\right)}^{2}$

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

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

$x = - 25$

and

$x = 4$

However, we will not accept $x = - 25$ as an answer because it will yield an imaginary number in the original equation. The squaring step (step1b) created this extra root.