Question

Solve the following equation using the square root property.

Answer 1

Answer:

$\frac{i\sqrt{5} }{3} , -\frac{i\sqrt{5} }{3}$

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:

$9x^2+10=5\\9x^2=5-10\\9x^2=-5\\x^2=\frac{-5}{9}$

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:

$x=\sqrt\frac{-5}{9}= \frac{\sqrt{-5} }{\sqrt{9}} = \frac{\sqrt{-5} }{3}$

$x=-\sqrt\frac{-5}{9}= -\frac{\sqrt{-5} }{\sqrt{9}} = -\frac{\sqrt{-5} }{3}$

We notice that the numerator on the right side renders the square root of a NEGATIVE number (-5). This originates the imaginary unit "i":

$x=\frac{i\sqrt{5} }{3} \\x=-\frac{i\sqrt{5} }{3}$

Therefore the correct answer is the third listed option in your pasted image