If $\displaystyle z=x+yi$ and $\displaystyle z^2=a+bi$ , x,y,a,b are all real numbers . Prove that $\displaystyle 2x^2=\sqrt{(a^2+b^2)}+a$

By solving the equation $\displaystyle z^4+6z^2+25=0$ for $\displaystyle z^2$ or otherwise , express each root of the equation in the form of $\displaystyle x+yi$