Respuesta :
Given:
The quadratic equation is [tex]x^{2}=-5 x-3[/tex]
We need to determine the solutions of the quadratic equation.
Solution:
Let us solve the equation to determine the value of x.
Adding both sides of the equation by 5x and 3, we get;
[tex]x^{2}+5 x+3=0[/tex]
The solution of the equation can be determined using quadratic formula.
Thus, we get;
[tex]x=\frac{-5 \pm \sqrt{5^{2}-4 \cdot 1 \cdot 3}}{2 \cdot 1}[/tex]
[tex]x=\frac{-5 \pm \sqrt{25-12}}{2 }[/tex]
[tex]x=\frac{-5 \pm \sqrt{13}}{2 }[/tex]
Thus, the two roots of the equation are [tex]x=\frac{-5 + \sqrt{13}}{2 }[/tex] and [tex]x=\frac{-5- \sqrt{13}}{2 }[/tex]
Hence, the solutions of the equation are [tex]x=\frac{-5 + \sqrt{13}}{2 }[/tex] and [tex]x=\frac{-5- \sqrt{13}}{2 }[/tex]
