Answer:
[tex]x=5+\sqrt{12}[/tex]
or
[tex]x=5-\sqrt{12}[/tex]
Step-by-step explanation:
[tex]x^2-10x+13=0[/tex]
[tex]x^2-10x=-13[/tex]
[tex]x^2-10x+(\frac{10}{2})^2 =-13+(\frac{10}{2})^2[/tex]
[tex]x^2-10x+(5)^2=-13+(5)^2[/tex]
[tex]x^2-10x+25=-13+25\\x^2-10x+25=12[/tex]
Factor.
[tex](x-5)^2=12[/tex]
Extract the square root.
[tex]x-5=\frac{+}{} \sqrt{12}[/tex]
Add 5
[tex]x=5+\sqrt{12}[/tex]
or
[tex]x=5-\sqrt{12}[/tex]
