what are the values of x in the equation x² - 6x + 9 = 25?\no x = -2 or x = 8\no x = -1 or x = -11\no x = 1…

Explanation:

Step1: Recognize perfect - square trinomial

The left - hand side of the equation $x^{2}-6x + 9$ is a perfect - square trinomial. It can be factored as $(x - 3)^{2}$. So the equation becomes $(x - 3)^{2}=25$.

Step2: Take square root of both sides

Taking the square root of both sides, we get $x−3=\pm\sqrt{25}$. Since $\sqrt{25}=5$, the equation splits into two: $x - 3=5$ and $x - 3=-5$.

Step3: Solve for x in each equation

For $x - 3=5$, adding 3 to both sides gives $x=5 + 3=8$. For $x - 3=-5$, adding 3 to both sides gives $x=-5 + 3=-2$.

Answer:

A. $x=-2$ or $x = 8$