Answer:
[tex]x=\frac{7+\sqrt{65}}{2}, x=\frac{7-\sqrt{65}}{2}[/tex]
Step-by-step explanation:
We are given that a quadratic equation
[tex]x^2=7x+4[/tex]
[tex]x^2-7x-4=0[/tex]
We have to find the solutions of the quadratic equation.
a=1, b=-7,v=-4
Quadratic formula:[tex]x=\frac{-b\pm\sqrt{b^2-4ac}{2a}[/tex]
Substitute the values in the quadratic formula
[tex]x=\frac{-(-7)\pm\sqrt{(-7)^2-4(1)(-4)}}{2(1)}[/tex]
[tex]x=\frac{7\pm\sqrt{49+16}}{2}[/tex]
[tex]x=\frac{7\pm\sqrt{65}}{2}[/tex]
[tex]x=\frac{7+\sqrt{65}}{2}, x=\frac{7-\sqrt{65}}{2}[/tex]
Hence, the solutions of quadratic equation are
[tex]x=\frac{7+\sqrt{65}}{2}, x=\frac{7-\sqrt{65}}{2}[/tex]
