Answer:
[tex]x=\frac{-7-\sqrt{17}}{2}\textrm{ or }x=\frac{-7+\sqrt{17}}{2}[/tex]
Step-by-step explanation:
Given:
The equation is given as:
[tex]x^2=-7x-8[/tex]
Rearrange the above equation in standard quadratic equation of the form [tex]ax^2+bx+c=0[/tex]
Adding [tex]7x + 8[/tex] on both sides, we get
[tex]x^2+7x+8=0[/tex]
Here, [tex]a=1,b=7,c=8[/tex]
Now, we solve this using quadratic formula,
[tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\x=\frac{-7\pm \sqrt{7^2-4(1)(8)}}{2(1)}\\x=\frac{-7\pm \sqrt{49-32}}{2}\\x=\frac{-7\pm \sqrt{17}}{2}\\\\\\\therefore x=\frac{-7-\sqrt{17}}{2}\textrm{ or }x=\frac{-7+\sqrt{17}}{2}[/tex]
