# How do you solve 5(sqrt x) - x =6?

Feb 2, 2016

$5 \left(\sqrt{x}\right) - x = 6$

$\rightarrow 5 \left(\sqrt{x}\right) = 6 + x$

$\rightarrow \sqrt{x} = \frac{6 + x}{5}$

Square both sides to remove the radical sign:

$\rightarrow {\left(\sqrt{x}\right)}^{2} = {\left(\frac{6 + x}{5}\right)}^{2}$

$\rightarrow x = \left(\frac{6 + x}{5}\right) \left(\frac{6 + x}{5}\right)$

$\rightarrow x = \frac{36 + 6 x + 6 x + {x}^{2}}{25}$

$\rightarrow x = \frac{36 + 12 x + {x}^{2}}{25}$

Cross multiply:

$\rightarrow 25 x = 36 + 12 x + {x}^{2}$

Subtract $12 x$ both sides:

$\rightarrow 13 x = 36 + {x}^{2}$

Subtract $13 x$ both sides:

$\rightarrow 0 = 36 + {x}^{2} - 13 x$

Write the equation in Standard form:

$\rightarrow {x}^{2} - 13 x + 36 = 0$

Luckily it Factors to:

$\rightarrow \left(x - 9\right) \left(x - 4\right) = 0$

So,$x = 9 , 4$