we have
[tex] x^{2} =-13x-4\\ x^{2} +13x+4=0 [/tex]
we know /that
Since you can not get the roots by easily factoring the equation, you have to use the quadratic equation.
The quadratic equation is
[tex] x=(-b + /-\sqrt{(b^{2}-4ac)} )/(2a) [/tex]
in this problem
[tex] a=1\\ b=13\\ c=4 [/tex]
substitute in the equation
[tex] x=(-13 + /-\sqrt{(13^{2}-4*1*4)} )/(2) [/tex]
[tex] x=(-13 + /-\sqrt{(153)} )/(2) [/tex]
the roots are
[tex] x1=(-13 + \sqrt{(153)} )/(2) [/tex]
[tex] x2=(-13 -\sqrt{(153)} )/(2) [/tex]
[tex]x1=(- \frac{13}{2} )+( \frac{3}{2} )* \sqrt{17} [/tex]
[tex]x2=(- \frac{13}{2} )-( \frac{3}{2} )* \sqrt{17} [/tex]
