Answer:
Option 3 and 4 - 0,-13
Step-by-step explanation:
Given : Expression [tex]x^2=-13x-4[/tex]
To find : What are the solutions?
Solution :
The quadratic formula of the quadratic equation [tex]ax^2+bx+c=0[/tex] is
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Comparing with general equation, [tex]x^2+13x+4=0[/tex]
where, a=1 ,b=13, c=4
Substitute in the formula,
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
[tex]x=\frac{-13\pm\sqrt{13^2-4(1)(4)}}{2(1)}[/tex]
[tex]x=\frac{-13\pm\sqrt{169-16}}{2}[/tex]
[tex]x=\frac{-13\pm\sqrt{153}}{2}[/tex]
[tex]x=\frac{-13+\sqrt{153}}{2},\frac{-13-\sqrt{153}}{2}[/tex]
The value of x is [tex]x=-0.315,-12.68[/tex]
Approximately the solution of the expression is x=0,-13.
