Answer:
[tex]x_{1}=\frac{-13+\sqrt{153}}{2}\\x_{2}=\frac{-13-\sqrt{153}}{2}[/tex]
Step-by-step explanation:
The given expression is
[tex]x^{2}=-13x-4[/tex]
To solve this quadratic equation, we first need to place all terms in one side of the equation sign
[tex]x^{2} +13x+4=0[/tex]
Now, to find all solutions of this expression, we have to use the quadratic formula
[tex]x_{1,2}=\frac{-b\±\sqrt{b^{2}-4ac}}{2a}[/tex]
Where [tex]a=1[/tex], [tex]b=13[/tex] and [tex]c=4[/tex]
Replacing these values in the formula, we have
[tex]x_{1,2}=\frac{-13\±\sqrt{(13)^{2}-4(1)(4)}}{2(1)}\\x_{1,2}=\frac{-13\±\sqrt{169-16}}{2}=\frac{-13\±\sqrt{153}}{2}[/tex]
So, the solutions are
[tex]x_{1}=\frac{-13+\sqrt{153}}{2}\\x_{2}=\frac{-13-\sqrt{153}}{2}[/tex]
If we approximate each solution, it would be
[tex]x_{1}=\frac{-13+\sqrt{153}}{2}\approx -0.32\\\\x_{2}=\frac{-13-\sqrt{153}}{2} \approx -12.68[/tex]
