Question

Solve the radical equation. square root of 8x+9=x+2

Answer 1

Answer:x=-1

Step-by-step explanation:

Answer 2

Answer:

D. There are no extraneous solutions to the equation.

Step-by-step explanation:

We have been given an equation $\sqrt{8x+9}=x+2$. We are asked to find extraneous solution to the radical equation.

First of all, we will square both sides of our given equation as:

$(\sqrt{8x+9})^2=(x+2)^2$

$8x+9=x^2+4x+4$

Upon switching the sides, we will get:

$x^2+4x+4=8x+9$  

$x^2+4x-8x+4=8x-8x+9$  

$x^2-4x+4=9$  

$x^2-4x+4-9=9-9$  

$x^2-4x-5=0$  

Upon splitting the middle term:

$x^2-5x+x-5=0$  

$x(x-5)+1(x-5)=0$  

$(x-5)(x+1)=0$  

Using zero product property, we will get:

$(x-5)=0\text{ (or) }(x+1)=0$  

$x=5 \text{ (or) }x=-1$  

Now, we will check both solutions to find any extraneous solution as:

$\sqrt{8x+9}=x+2$

$\sqrt{8(-1)+9}=-1+2$

$\sqrt{-8+9}=1$

$\sqrt{1}=1$

$1=1$ True.

$\sqrt{8x+9}=x+2$

$\sqrt{8(5)+9}=5+2$

$\sqrt{40+9}=7$

$\sqrt{49}=7$

$7=7$ True.

Therefore, there is no extraneous solution to our given equation and option D is the correct choice.