# How do you solve x-1= sqrt( 6x+10)?

Nov 7, 2016

$x = 9$.

#### Explanation:

${\left(x - 1\right)}^{2} = {\left(\sqrt{6 x + 10}\right)}^{2}$

${x}^{2} - 2 x + 1 = 6 x + 10$

${x}^{2} - 8 x - 9 = 0$

$\left(x - 9\right) \left(x + 1\right) = 0$

$x = 9 \mathmr{and} x = - 1$

However, since extraneous solutions are a distinct possibility, let's check our solution inside the initial equation.

9 - 1 =^? sqrt(6 xx 9 + 10)

8 = 8" "color(green)(√)

AND

-1 - 1=^? sqrt(6 xx -1 + 10)

$- 2 \ne 2 \text{ } \textcolor{red}{\times}$

Hence, the only true solution is $x = 9$.

Hopefully this helps!