Find all real solutions of the equation. $\sqrt { 5 x + 9 } + 3 = x$
A) 0
B) 0, 11
C) 11
D) 1, 0
E) -11

Question

Quizplus · Accepted Answer

First, we see that $x\geq -	frac{9}{5}$ in order for $\sqrt{5x+9}$ to be defined. Rewriting the equation by subtracting 3 from both sides and then squaring both sides gives $x^2-6x+9=5x+9$, or $x^2-11x=0$. Then, $x=0$ or $x=11$, but we need to check if they satisfy $x\geq -	frac{9}{5}$. Clearly $11\geq -	frac{9}{5}$, but $0
ot\geq -	frac{9}{5}$. Therefore, the only solution is $x=\boxed{	extbf{(C)}\ 11}$.

Find All Real Solutions of the Equation 5x+9+3=x\sqrt { 5 x + 9 } + 3 = x5x+9​+3=x

Find All Real Solutions of the Equation $\sqrt { 5 x + 9 } + 3 = x$