what are the values of x in the equation $x^{2}-6x + 9 = 25$?\n$x=-2$ or $x = 8$\n$x=-1$ or $x=-11$\n$x = 1$…

what are the values of x in the equation $x^{2}-6x + 9 = 25$?\n$x=-2$ or $x = 8$\n$x=-1$ or $x=-11$\n$x = 1$ or $x = 11$\n$x = 2$ or $x=-8$

what are the values of x in the equation $x^{2}-6x + 9 = 25$?\n$x=-2$ or $x = 8$\n$x=-1$ or $x=-11$\n$x = 1$ or $x = 11$\n$x = 2$ or $x=-8$

Answer

Explanation:

Step1: Rewrite the left - hand side as a perfect square.

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

Step2: Take the square root of both sides.

We get $x - 3=\pm\sqrt{25}$, so $x - 3=\pm5$.

Step3: Solve for $x$ in two cases.

Case 1: When $x - 3 = 5$, then $x=5 + 3=8$. Case 2: When $x - 3=-5$, then $x=-5 + 3=-2$.

Answer:

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