Respuesta :
We have that the quadratic expression is given by:
[tex](x-6)^2=9[/tex]If we apply the square root to both sides of the equation, we have:
[tex]\sqrt[]{(x-6)^2}=\pm\sqrt[]{9}[/tex]As we can see, we will have two solutions. Then, we have:
[tex](x-6)=\pm3_{}[/tex]Then, we have the two possible solutions as follows:
[tex]x-6=3,x-6=-3[/tex]And we need to solve for both of them as follows:
First case
1. We need to add 6 to both sides of the equation:
[tex]x-6=3\Rightarrow x-6+6=3+6\Rightarrow x=9[/tex]Second case
2. We need to add 6 to both sides of the equation:
[tex]x-6=-3\Rightarrow x-6+6=-3+6\Rightarrow x=3_{}[/tex]Therefore, in summary, the exact answers are x = 9, and x = 3.
