Question

What is the resulting equation when (x-6)(x+2)=9 is transformed by completing the square? (A) (x-2)²=25 B. (x-2)²=9 c. (x-2)²=3 D. (x-2)²=1

Answer 1

To transform the equation (x-6)(x+2)=9 by completing the square, first expand the equation, move constant term, add square of half the coefficient of x to both sides, and simplify to get (x-2)^2=25.

Step-by-step explanation:

To transform the equation (x-6)(x+2)=9 by completing the square, first expand the equation:

x^2 - 4x - 12 = 9

Now, move the constant term to the right side:

x^2 - 4x - 21 = 0

To complete the square, add the square of half the coefficient of x to both sides:

x^2 - 4x + 4 - 21 = 4

This simplifies to:

(x-2)^2 = 25

So, the resulting equation is (x-2)^2=25. Therefore, the correct answer is (A) (x-2)²=25.