Question

Solve the following equation using the square root property.

Answer 1

`(i√(5) )/(3) , -(i√(5) )/(3)`

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=(-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(-5)/(9)= (√(-5) )/(√(9)) = (√(-5) )/(3)`

`x=-\sqrt(-5)/(9)= -(√(-5) )/(√(9)) = -(√(-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=(i√(5) )/(3) \\x=-(i√(5) )/(3)`

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