Question

Given that $z^2-10z+25=9$, what is $z$?

• A. $3,4$
• B. $1,6$
• C. $2,6$
• D. $2,8$

Answer 1

The correct option is D $2,8$

$\{2,8\}$

Since you recognize that the left hand side of the equation is a perfect square quadratic, you will factor the left side of the equation first, instead of trying to set everything equal to $0$

$z^2-10z+25=9$

${(z-5)}^2=9$

$\sqrt{{(z-5)}^2}=\sqrt{9}$

$z-5=\pm 3$

$z=5\pm 3$