Answer:
[tex]x_1=\frac{7+\sqrt{65}} {2}[/tex]
[tex]x_2=\frac{7-\sqrt{65}} {2}[/tex]
Step-by-step explanation:
we know that
The formula to solve a quadratic equation of the form
[tex]ax^{2} +bx+c=0[/tex]
is equal to
[tex]x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}[/tex]
in this problem we have
[tex]x^{2}=7x+4[/tex]
equate to zero
[tex]x^{2}-7x-4=0[/tex]
so
[tex]a=1\\b=-7\\c=-4[/tex]
substitute in the formula
[tex]x=\frac{-(-7)\pm\sqrt{-7^{2}-4(1)(-4)}} {2(1)}[/tex]
[tex]x=\frac{7\pm\sqrt{65}} {2}[/tex]
therefore
[tex]x_1=\frac{7+\sqrt{65}} {2}[/tex]
[tex]x_2=\frac{7-\sqrt{65}} {2}[/tex]
StartFraction 7 minus StartRoot 65 EndRoot Over 2 EndFraction comma StartFraction 7 + StartRoot 65 EndRoot Over 2 EndFraction
