Answer
No solution
Work Step by Step
Given:
$\sqrt {-14-9x}=x$
Squaring both sides, we have
$-14-9x=x^{2}$
Adding $14$ and $9x$ to both sides, we get
$0=x^{2}+9x+14$
Factoring, we get
$(x+7)(x+2)=0$
Using the Zero-product property, we obtain
$x=-7$ or $x=-2$.
Let's check the results.
When $x=-7$,
$\sqrt {-14-9(-7)}=\sqrt {49}=7\ne-7$
When $x=-2$,
$\sqrt {-14-9(-2)}=\sqrt {4}=2\ne-2$
Neither $x=-7$, nor $x=-2$ satisfies the original equation, they are extraneous solutions. There is no solution for the equation.
