Answer: x=-3
Step-by-step explanation:
First let's eliminate the square root
[tex](\sqrt{x^2-5x+2})^2=(\sqrt{x^2+17})^2\\x^2-5x+2=x^2+17[/tex]
Now subtract [tex]x^2\\[/tex] from both sides
[tex]x^2-5x+2-x^2=x^2+17-x^2\\-5x+2=17[/tex]
Subtract 2 from both sides
[tex]-5x+2-2=17-2\\-5x=15[/tex]
Finally divide both sides by -5
[tex]\frac{-5x}{-5} =\frac{15}{-5} \\x=-3[/tex]
