Answer:
[tex]5+2\sqrt{31[/tex] and [tex]5-2\sqrt{31[/tex]
Step-by-step explanation:
First move everything to the same side:
[tex]6=x^2-10x[/tex] ---> [tex]x^2-10x-6=0[/tex]
Then use the quadratic formula:
x= (-b ± [tex]\sqrt{b^2 -4ac}[/tex])/2a
[tex]a=1\\b=-10 \\c=-6[/tex]
x= (-(-10) ± [tex]\sqrt{-10^2 -4*1*-6}[/tex])/2*1
x= (10 ± [tex]\sqrt{100+24}[/tex])/2
Solution 1:
(10 + [tex]\sqrt{1 24}[/tex])/2
[tex]\frac{10+2\sqrt{31} }{2}[/tex]= [tex]5+2\sqrt{31[/tex]
Solution 1:
(10 - [tex]\sqrt{1 24}[/tex])/2
[tex]\frac{10-2\sqrt{31} }{2}[/tex]= [tex]5-2\sqrt{31[/tex]
