Solve the following equation using the square root property.

Answer:[tex]\frac{i\sqrt{5} }{3} , -\frac{i\sqrt{5} }{3}[/tex]Step-by-step explanation:Since this quadratic equation does not contain a term in x, we can proceed to isolate the term with the unknown on the left hand side, by subtracting 10 from both sides, and then dividing both sides by 9 as shown below:[tex]9x^2+10=5\\9x^2=5-10\\9x^2=-5\\x^2=\frac{-5}{9}[/tex]Now we apply the square root on both sides to get the value/s for x that make the equation true. Remember to consider plus and minus signs to take care of the two possible solutions involved in the root, so let's do each case separately:[tex]x=\sqrt\frac{-5}{9}= \frac{\sqrt{-5} }{\sqrt{9}} = \frac{\sqrt{-5} }{3}[/tex][tex]x=-\sqrt\frac{-5}{9}= -\frac{\sqrt{-5} }{\sqrt{9}} = -\frac{\sqrt{-5} }{3}[/tex]We notice that the numerator on the right side renders the square root of a NEGATIVE number (-5). This originates the imaginary unit "i":[tex]x=\frac{i\sqrt{5} }{3} \\x=-\frac{i\sqrt{5} }{3}[/tex]Therefore the correct answer is the third listed option in your pasted image