first you subtract 17 from both sides. [tex] x^{2} -10x+25-17=17-17
x^{2} -10x+8=0[/tex]
Then you use the quadratic formula
[tex]x1,2 = \frac{-b± \sqrt{b^2-4ac} }{2a} [/tex] for get about what is in between -b and ±.
a=1 b=-10 c=8
first answer [tex] \frac{10+ \sqrt{-10^2-4(1)(8)} }{2(1)} [/tex]
do the work that is under the sqrt sign. [tex]-10^2-4(1)(8)=68
-10^2=100
-4(1)(8)=32
100-32=68[/tex]
[tex]10+ \sqrt{68} [/tex]
[tex] \frac{10+ \sqrt{68} }{2} = \frac{10+2 \sqrt{17} }{2} [/tex]
divide 10 by 2 and cancel out the 2's
[tex]5+ \sqrt{17} [/tex] is the first answer
you do the same thing for the second answer but instead of b+ it is b+
The second answer is [tex]5- \sqrt{17} [/tex]
