# Thread: [HELP] Solving Complex solutions of Quadratic Equations

1. ## [HELP] Solving Complex solutions of Quadratic Equations

Anyone knows how to solve this problem?

Find all solutions of the equation and express them in form of a+bi

1.x² + 9 = 0

2.9x² + 4 = 0

3.x² +1/2x + 1 = 0

I really have no idea what to do..

Thanks in advance!

2. ## Re: [HELP] Solving Complex solutions of Quadratic Equations

Do you not know how to take square roots? If $x^2+ 9= 0$ then $x^2= -9$ and you take the square root of both sides.

If $9x^2+ 4= 0$, then $9x^2= -4$, $x^2= -\frac{4}{9}$. Of course, you need to know that the square root of -1 is "i".

For the last one, I presume that is $x^2+ (1/2)x+ 1= 0$. Do you know the "quadratic formula"? If $ax^2+ bx+ c= 0$, then $x= \frac{-b\pm\sqrt{b^2- 4ac}}{2a}$. Here a= 1, b= 1/2, c= 1. $x= \frac{-1/2\pm \sqrt{1/4- 4}}{2}= \frac{-1/2\pm \sqrt{-15/4}}{2}= -\frac{1}{4}\pm\frac{\sqrt{-15}}{4}= -\frac{1}{4}\pm \frac{\sqrt{15}}{4}i$.

3. ## Re: [HELP] Solving Complex solutions of Quadratic Equations

Thank you man! Really help me!!