ANSWER:
(a) 3
(b) -6
STEP-BY-STEP EXPLANATION:
We have the following equation:
[tex]\sqrt{x+22}=x+2[/tex]
We solve for x:
[tex]\begin{gathered} \left(\sqrt{x+22}\right)^2=\left(x+2\right)^2 \\ \\ x+22=x^2+4x+4 \\ \\ x^2+4x-x+4-22=0 \\ \\ x^2+3x-18=0 \\ \\ \left(x-3\right)\left(x+6\right)=0 \\ \\ x-3=0\rightarrow x=3 \\ \\ x+6=0\rightarrow x=-6 \\ \\ \text{ We check the solutions} \\ \\ \sqrt{3+22}=3+2\rightarrow\sqrt{25}=5\rightarrow5=5\rightarrow\text{ True} \\ \\ \sqrt{\left(-6\right)+22}=\left(-6\right)+2\rightarrow\sqrt{16}=-4\rightarrow4=-4\rightarrow\text{ False} \end{gathered}[/tex]
Therefore:
(a) The only correct answer is x = 3
(b) The extraneous response is x = -6
