Answer:
[tex](4-\sqrt{19},4+\sqrt{19)[/tex]
Step-by-step explanation:
we have
[tex]x^{2} -8x=3[/tex]
Divide the coefficient of term x by 2
[tex]-8/2=-4[/tex]
Squared the number
[tex](-4)^2=16[/tex]
Adds the number 16 to the both sides
[tex]x^{2} -8x+16=3+16[/tex]
[tex]x^{2} -8x+16=19[/tex]
Rewrite as perfect squares
[tex](x-4)^{2}=19[/tex]
take square root both sides
[tex](x-4)=(+/-)\sqrt{19}[/tex]
[tex]x=4(+/-)\sqrt{19}[/tex]
[tex]x_1=4(+)\sqrt{19}[/tex]
[tex]x_2=4(-)\sqrt{19}[/tex]
therefore
The solution set is
[tex](4-\sqrt{19},4+\sqrt{19)[/tex]
