Answer: D is the right answer. The solution set of the given equation={-2,10}.
Explanation:
Given equation: [tex]x^2-8x=20[/tex]
The standard perfect square trinomial equation is [tex]x^2+2ax+a^2=(x+a)^2[/tex]
On comparing this with the left side of the given equation ,we get 2a=-8
⇒a= -4 and [tex]a^2=16[/tex]
Now to make given equation perfect square add 16 on the both sides, we get [tex]x^2-8x+16=20+16\\\Rightarrow(x-4)^2=36[/tex]
Taking square root on both the sides we get,
[tex]x-4=-6\ or\ x-4=6[/tex]
add 4 on both sides, we get
⇒x= -6+4 or x=6+4
⇒x=-2 or x=10
Therefore, the solution set of the given equation={-2,10}.
Thus D is the right answer.
